I don't think I know any that are communist per se (except maybe the Chinese one about Karl Marx, but I haven't gotten around to actually watch it) but I can recommend some with strong leftist themes:

Code Geass is basically Reform or Revolution - the anime.

Psycho Pass is a cyberpunk dystopia with a police force that tries to prevent crimes before they happen (and a super heavy criticism on why that is a majorly stupid idea)

Princess Principal is a steampunk spy drama set in a alternate universe london, where a proletarian revolution of some kind has split the city in two. It can be a bit lib at times but I absolutely love this show.