Colten Boushie's family members say they believe the Liberal government will go the distance and change what they see as systemic problems with Canada's justice system in the simmering aftermath of his shooting death.

"This ain't going to stop until something changes for the better," Debbie Baptiste told reporters Tuesday, just days after Saskatchewan farmer Gerald Stanley was found not guilty in her son's shooting death.

Colten Boushie's mother and cousin say their message that change is needed was heard on Parliament Hill. 1:36

Baptiste and other members of Boushie's family are in Ottawa this week for high-level meetings, including one with Prime Minister Justin Trudeau early in the afternoon.

Prime Minister Justin Trudeau is set to deliver a speech in the House of Commons after question period Wednesday on the recognition and implementation of Indigenous rights.

The family said that, so far, the meetings have been engaging and respectful.

"The most significant thing is that there was a general consensus that there are systemic issues regarding Indigenous people in the judicial system and that each person has promised to work with us to make concrete changes," said Boushie's cousin Jade Tootoosis.

"That's exactly what we came here for."

Lawyer Eleanore Sunchild, who accompanied the family to Parliament Hill, said one of the things they're asking for is a change to the way jurors are chosen in Canada.

Reforms coming

Under Canada's Criminal Code, peremptory challenges allow defence lawyers and Crown prosecutors in a second-degree murder case to reject as many as 12 people from a jury without giving any reason. Critics say the long-standing procedure can lead to discrimination against potential jurors — and can deliver a jury that is biased or lacks understanding of Indigenous cultural and social customs.

Some observers have argued the jury process in Boushie's case was biased because the defence team excluded five potential jurors who appeared to be Indigenous. CBC News has not independently determined the reason for their exclusion.

"Even though people say this wasn't a case about race, it was because of how these people were excluded right from the beginning," said Sunchild.

Justice Minister Jody Wilson-Raybould has been tasked with reviewing the criminal justice system — including sentencing, trial delays, the overrepresentation of Indigenous people in prisons and so-called 'peremptory challenges'.

"Those reforms are coming. The reality of the Boushie family coming here and the elevation of the national consciousness on the challenges and systemic barriers that marginalize people facing the criminal justice system is very welcome," Wilson-Raybould said after her meeting with the Boushie family.

She said reforms are coming "soon" but wouldn't offer a timeline.

Chris Murphy, the Boushie family's friend and lawyer, said he believes the government will go "pretty far" in making changes to the jury selection process.

NDP Leader Jagmeet Singh said he's debating whether his party should be in favour of abolishing peremptory challenges.

NDP Leader Jagmeet Singh says that the 'not guilty' verdict in the Colten Boushie case perpetuates the idea that indigenous lives have no value. 1:32

"It's a discussion we need to have," he said.

"There is underrepresentation of equity-seeking people on juries. That is something people have noted for a long time. In particular, Indigenous people are very underrepresented in jury selection and juries in general."

Singh said he's used peremptory challenges in his career as a criminal defence lawyer.

Defends tweet

On Friday, Trudeau said he couldn't imagine "the grief and sorrow" the Boushie family feels.

The justice minister also took to Twitter, arguing that "as country we can and must do better. I am committed to working everyday to ensure justice for all Canadians."

A number of Conservative MPs cautioned the Liberal government against tweeting about the verdict.

"We need to let the many steps of an independent judicial process unfold without political interference," Conservative Indigenous affairs critic Cathy McLeod wrote on Twitter.

On Tuesday, Wilson-Raybould defended her tweet.

"What I know even more so now than when I sent out that tweet is that for not just Indigenous Canadians across the country but Canadians who are speaking out on the challenges that we face in the criminal justice system, protesting on the streets," she said.

"To have an attorney general who doesn't recognize that or acknowledge it would be deeply concerning."

Wilson Raybould on her tweet and the Boushie verdict 1:30

The family will meet with Singh on Tuesday and senators Kim Pate and Murray Sinclair on Wednesday. They said they haven't met with anyone from the Conservative party, but are open to it.

Murphy said he's been in contact with Conservative MP Rosemarie Falk, who represents the area the Boushie and Stanley families are from.

Boushie was shot and killed after he and four others from the Red Pheasant Cree Nation drove onto Stanley's rural property in an SUV in August 2016.

Eric Meechance, who was in the SUV with Boushie that day, told the court he tried to start an ATV on Stanley's property but denied trying to steal it.

When Stanley's son hollered at them, one of Boushie's other friends tried to drive away, but Stanley's son smashed the SUV's window with a hammer and the vehicle crashed. Stanley fired shots from a pistol as two of the friends ran from the vehicle.

Boushie was shot in the head while still in the SUV. Stanley testified he never meant to shoot anyone and that the handgun he was holding went off a third time, accidentally, when he tried to reach for the keys to the SUV.

The jury had the option of finding Stanley guilty of second-degree murder or manslaughter, or not guilty, according to Chief Justice Martel Popescul, who presided over the trial.