West Yorkshire Police said: "The distraction burglary was involving a number of individuals, and happened at a residential property on Bywell Road on January 29.
"The incident happened at around 5.15pm, when the suspects entered a shop attached to the property.
"Some of the suspects remained in the commercial premises and distracted those working in the shop.
"Several other suspects then entered the residential property next door.
"They made a search of the property and made off with a large quantity of cash and jewellery."
Detectives are asking anyone who recognises those pictured to contact police as they may have information valuable to the investigation.
A 32-year-old woman has previously been arrested in connection with the incident and released while the investigation continues.
Anyone with information is asked to contact Kirklees CID on 101, quoting crime reference 13190053080.
Those wishing to remain anonymous can also pass information to independent charity Crimestoppers on 0800 555 111.