Ashley, who is not a criminal but has an intellectual disability, a schizophrenic illness and can be violent, has lived at the Tawhirimatea mental health unit in Porirua for five years.
He sleeps in a 10m-square room with just a mattress and a urine bottle, and when staff order it, can be locked in for long periods - despite repeated warnings from multiple agencies that his condition is deteriorating, and his treatment breaches human rights.
His case is subject to a "watching brief" from the Ombudsman's torture inspectors who recently labelled his living situation "cruel, inhuman or degrading", prompting fresh calls for him to be removed from near-permanent seclusion.
The petition is calling for the Mr Coleman to intervene under Section 32 of the Public Health and Disability Act 2000.
"We request that Ashley Peacock be urgently relocated to an individualised service in the community with appropriate levels of support, with a clear time frame," it said.
So far the Government has defended Ashley's treatment, saying his case is "complicated" and safety was paramount.
The Capital and Coast District Health Board has previously said he had some of the "highest and most complex needs" and had issues with unpredictable violence.
"This situation is not ideal for the client, other residents or staff," general manager of mental health, addictions and disability services, Nigel Fairley, said.
"We are hopeful a solution may soon be found for this client."