Mother-of-two Jean Campbell was last seen walking her dog and heading towards Cranhill Park in the east end of Glasgow on the night of Friday December 13.
Her body was discovered at around 7.40am the next day by her husband who had gone out to search for her.
Police Scotland Detective Chief Inspector Colin Carey said: "A dedicated team of highly experienced detectives are working round the clock on this inquiry. Despite previous media appeals and a scene revisit, we have still to identify a motive for this brutal murder.
"We are issuing a CCTV image of Jean Campbell which was captured at 2230 hours on Friday 13 December as she was walking along Bellrock Street in the direction of Cranhill Park with her German shepherd dog Kai. This is the last known sighting of Jean Campbell.
"If anyone remembers seeing Jean that night, or recognises her description, I would ask them to contact us as a matter of urgency.
"The person responsible for this crime may have sustained minor injuries to their face or body and may be acting out of character. There is a possibility their clothing may be dirty or stained with muck or grass and again I would ask if anyone who has any suspicions regarding friends, neighbours or family members who came home late on the evening of Friday 13 December or early hours of Saturday 14 December with unexplained injuries or dirt-stained clothing to contact the police."
Mrs Campbell was wearing pyjama bottoms and a black, three-quarter-length jacket with a hood.
Mr Carey said: "The local community has been keen to assist police. However, I am sure there are people who have information that could assist our investigation who, for whatever reason, have yet to contact police.
"If you have any information whatsoever that may assist the inquiry, no matter how insignificant you think it is, please come forward and share that information with us.
"I would also like to reassure local people that there are extra police patrols in the area, and anyone with any concerns should speak to officers.
Crimestoppers is offering a reward of up to £5,000.
A spokesman for the charity said: "This is a tragic ordeal for the family of Jean to have to go through and they deserve answers as to why this has happened and who is responsible.
"The person or people who committed this murder should not be allowed to get away with their actions and, for this reason, we would urge anyone with information to come forward and contact Crimestoppers anonymously, safe in the knowledge nobody will ever know you spoke to us."