The man who painted offensive graffiti beside a memorial to comedian Eurydice Dixon in Melbourne's Princes Park is appealing against his conviction and sentence, despite pleading guilty.

Key points: Andrew Nolch was sentenced to an 18-month community corrections order and ordered to pay almost $20,000 in restitution last month

Andrew Nolch was sentenced to an 18-month community corrections order and ordered to pay almost $20,000 in restitution last month He is now appealing against his sentence and conviction claiming he had "an incompetent lawyer"

He is now appealing against his sentence and conviction claiming he had "an incompetent lawyer" Outside court, Nolch said he was "sorry for the harm" he had caused Eurydice Dixon's family

Andrew Nolch, 29, has apologised publicly for the first time for painting a lewd symbol on a soccer field at the park, just hours before 10,000 people gathered for a vigil in Ms Dixon's honour.

After launching his appeal in the Victorian County Court, Nolch made a qualified apology to Ms Dixon's family for causing them distress.

"I made a political statement and I am very political but, yeah, I'm definitely sorry for the harm I caused the family, the offence," he said outside court.

Ms Dixon's body was found by a passer-by on the playing field in the early hours of June 13 after she was attacked while walking home from a comedy gig. Jaymes Todd, 19, of Broadmeadows, has been charged with her rape and murder.

Nolch claims he had 'incompetent lawyer'

Nolch, of Bulleen in Melbourne's north-east, was sentenced in the Melbourne Magistrates' Court last month to an 18-month community corrections order.

He was also ordered to pay almost $20,000 in restitution and undertake 200 hours of community work.

But he is appealing against that sentence and conviction, claiming he thought he was pleading guilty to the lesser charge of making graffiti.

"I want to make it clear that I had an incompetent lawyer and that's why there was problems," he told the court.

"He offered to do the case for free and I think it was because he wanted media attention.

"So you pay peanuts, you get peanuts."

The appeal has been set down for February, when the court will be played an audio recording of the magistrates' court hearing as evidence of whether Nolch understood what charge he was pleading guilty to.

The prosecutor told the court that the police informant would also give evidence that Nolch had always agreed to plead guilty to the charge of criminal damage.

'Immeasurable' emotional damage

Nolch has indicated he will request the court be closed for the appeal to be heard.

County Court Judge Mark Taft said he would have "little sympathy" for that application, but it would be up to the judge who heard the appeal.

"It seems to me that the public interest in this case, as with all other cases, is wherever possible to have a transparent proceeding," he said.

Previously, Nolch's lawyer had argued the graffiti had been a political statement against feminism and the mainstream media.

But Magistrate Olivia Trumble, who sentenced Nolch, described that reasoning as "incomprehensible".

"Your intention was to have completed the vulgar image before the vigil commenced," Ms Trumble said.

"You wanted to cause as much outrage as possible.

"The emotional damage of your conduct is immeasurable."

Nolch will return to the County Court in November.