Gut epithelial cells have the highest proliferation rate in the human body (and probably mice too). They are essentially proliferating constantly, with complete turnover of the gut epithelium every 3-5 days.
One caveat, regarding the biostars question, is that these cells are also maturing (i.e. differentiating) into at least 5 different cell types that I can think of off the top of my head. However, I think the proliferation should only be occurring among the epithelial stem cells at the base of crypts, which differentiate as they mature and migrate towards the villi, so it might be possible to use single-cell sorting techniques to separate them for experimental purposes.
Another cool thing about the gut is that the entire structure of the epithelium (crypts, villi, cell differentiation, etc.) can be grown in vitro with various different primary cell culture systems.