What you describe is socialism, not Communism.
Under Communism there is no state. All things are owned in common. More precisely there is no property. So there would be no farm per se. People would just wander by and plant things for the good of the community. They might or might not stay around and harvest the crops. If they do, they have no more claim to eat that a bum in the gutter does.
In a Marxian fantasy world, people want to toil in the sun without reward because they care about the community. Under the absurd fantasy, there is so much produced by people with no incentive to produce that there is an abundance and no one worries about food or shelter. Free hotels that were built by people who just felt like it provide shelter for all. Free kitchens with cooks who just feel like making and serving food feed everyone. Someone will do the dishes just because they love the community.
That's a myth. This is from Chapter 2 of the Communist Manifesto:
The Communist revolution is the most radical rupture with traditional
property relations; no wonder that its development involved the most
radical rupture with traditional ideas.
But let us have done with the bourgeois objections to Communism.
We have seen above, that the first step in the revolution by the working
class is to raise the proletariat to the position of ruling class to win the
battle of democracy.
The proletariat will use its political supremacy to wrest, by degree, all
capital from the bourgeoisie, to centralise all instruments of production
in the hands of the State, i.e., of the proletariat organised as the ruling
class; and to increase the total productive forces as rapidly as possible.
Marx talks about degrees of communism where the state is in the first stages but, even then, he's not talking about the State as above and he's not talking about Socialism. He just assumes that the revolution will lead to a revolutionary government, as has always been the case. In his own fantasy, he talks about the State, as in the revolutionary government, will yield power and give the power to the proletariat (but he still calls them the proletariat, acknowledging that they're always the slaves to their labor) but even then, there is a State - the proletariat organized as the ruling class. Note the use of the word "ruling".
Like all communists, they lie about what Communism is - even Marx did it. But, like all communists, if you read their words you will find that they eventually tell what they're really trying to do.
