Morris was a member of the Head Hunters gang, along with his father and other friends and associates.
During his murder trial Murray told the jury he saw Morris, 27, attacking his younger brother and hit him in the head with a sickle-like tool, which he had retrieved from his home nearby.
He admitted killing Morris but denied the charge of murder saying he acted in defence of his brother.
After a two week trial a jury of eight men and four women found him guilty.
Lawyer Elizabeth Hall said there was a "real risk the outcome of this trial was affected unfairly and that a miscarriage of justice has occurred".
With the trial beginning around the anniversary of Morris' death there was a risk the "pre-trial publicity would crescendo at the commencement", Hall said.
Justice Rhys Harrison said the use of the word "crescendo" was "a bit extreme".
The other grounds Hall is appealing on are that the trial judge erred in his summing up when directing the jury on self defence and the jurors' exposure to "extraneous matters" risked the fairness of the trial.
Hall slammed actions of the police during the trial, saying officers were seen high-fiving members of the Head Hunters and "relaxing with, yes, the father of the victim, but also a man who was a senior member of the Head Hunters gang".
There were threats made of retribution, she said, and evidence given during the trial of intimidation by gang members.
There were a number of ways the risk could have been partly mitigated, she said, such as changing the venue, delaying the trial, and asking jury members at the start if they felt unable to consider the case in an unbiased way.
"The jury were expected to somehow steel themselves, knowing that their names were read out in court . . . knowing they were able to be observed throughout the two week trial."
Jury members were forced to "circulate" with members of the Head Hunters gang attending the trial, Hall said, as the layout of the court meant jurors could only enter and exit the courtroom through the public space of the courthouse.
Justice Harrison said no members raised any issues around such things with the foreperson.
Hall said there was a failure to protect the identities of the jurors. She pointed to a decision in Canada where jurors were obscured behind a screen to protect them from being seen by members of the public.
"In this case where there was a dangerous and intimidating gang involved . . . there was retribution, intimidation, death threats, it's my submission in this case there needed to be more thought put into ensuring that the jurors feel safe, not wait for there to be some contact and trying to deal with it afterwards."
Jurors had to move past Head Hunters as they came into the court, she said.
Lawyer for the Crown John Pike, QC, said it was a "grave matter" to allege a trial had been conducted unfairly.
"There has to be something really grave and weighty about the assertion," he told the court.
He said there was nothing to indicate the jury were swayed to sympathy for Millie Elder-Holmes by the high level of media attention given to the story, and so nothing to indicate the jury's decision had been biased by that sympathy.
"There is an over-emphasis, I would submit, on the drama underlying this trial."
Pike said Hall was asking the court to "speculate" that the overwhelming juror instinct would be sympathy, speculate what the impact of pre-trial media coverage would be, and speculate whether the judge's summing up and directions to the jury did not do enough to offset risks brought about by the media "frenzy".
