Private property isn't "anything you can own" here, it has a very specific meaning.
https://en.wikipedia.org/wiki/Personal_property#Personal_ver...
https://en.wikipedia.org/wiki/Personal_property#Personal_ver...
So one thing Marx did say is that he wanted money to be "superfluous". If money would be useless, how do you get to own a toothbrush? Does that mean we either go back to a barter economy, or something like a social points system like Seasame Credit?