Is modern Communism based on Marxism?
First, we have to figure out what we are going to call "modern communism." If we are talking about China, then I would argue that modern communism has little or nothing to do with Marxism. However, if we are talking about North Korea or Cuba, modern communism is based on Marxism, though it does not follow it completely.
Both North Korea and Cuba have very little in the way of private enterprise and private ownership. This is very much in keeping with Marxism. Although many Chinese companies are owned wholly or in part by the government, they are run more as capitalist companies than as state agencies. China also allows a great deal of purely private enterprise.
There are no countries in the world that have reached what Marx would have seen as the final stage of communism, but there are still a few countries that have systems based firmly on Marx's ideas.