So like I said in another comment, it would be the state-by-another-name that would sending someone to arrest me for paying someone to write code on my computer.
Because in the end it they will be owned by the state. You can assign it whatever other names you want, but it will be a state.
"workers who do the actual work at the plant own the means of production"
This cuts right to the heart of my original comment. That is a very broad model that simply doesn't apply to most workers, and numbers of whom grow smaller ever year. Marxism is an obsolete idea based on a world that hasn't existed for almost a century now.
It's clear that a factory is a "means of production to be owned by the state," but everything is unclear. A car, a hammer - even the computer you are reading this on can all be used as capital and lent to workers to apply their labor to. Would all home computers be controlled the Marxists?
Marxism is system that only makes sense at the very highest of levels (like the factory), but completely breaks down when looking at any kind of real implementation.
Unlike computer science, where all levels of abstraction ultimately derive from a solid base of boolean logic, there simply is no base to Marxism/Socialism/Communism/Anarchism.