

The important thing to understand is that even if you hate capitalism, neoclassical economics provide provides a pretty useful framework for analyzing and understanding it
It really doesn’t—which was Marx’s whole project as a critique of political economy, not “communist economics”, not “Marxist political economy”, etc.
But my point is that what people call a “market” in neoclassical economics is literally just any situation where you have a bunch of relatively autonomous groups of people all trying to accomplish various goals all interacting with each other
Communism abolishes the individual as economic subject, and the conflicts of interests found in a “market”. Communism abolishes exchange, and abolishes economies. So, no, there is no “market” in a communist mode of production, even by your definition.
The verb “maximising” suggests a measurable “utility” which can be “maximised”, rather than needs which are either met or not.