a communist country is one where there are non-state owned enterprises
Again, I implore you to actually read Marx. “Communism is when nobody owns a toothbrush” is just neoconservative propaganda. This isn’t what any AES state practices, much less what the more academic types believe.
Generating capital is definitely a feature of communism as long as it’s fictitious capital.
Nothing precludes you from generating ficticious capital in a communist system. Marxists simply recognize it as such, rather than deluding themselves into believing material value has been created when speculative asset prices rise.