Memes

You're correct in that it's about communal ownership of property, yes, but the idea that labor isn't rewarded proportionally is false. Higher skill or more intense labor creates more Value with respect to that which is required to create it. In Critique of the Gotha Programme, Marx explains what would likely happen as the means of production are sufficiently advanced:

But one man is superior to another physically, or mentally, and supplies more labor in the same time, or can labor for a longer time; and labor, to serve as a measure, must be defined by its duration or intensity, otherwise it ceases to be a standard of measurement. This equal right is an unequal right for unequal labor. It recognizes no class differences, because everyone is only a worker like everyone else; but it tacitly recognizes unequal individual endowment, and thus productive capacity, as a natural privilege. It is, therefore, a right of inequality, in its content, like every right. Right, by its very nature, can consist only in the application of an equal standard; but unequal individuals (and they would not be different individuals if they were not unequal) are measurable only by an equal standard insofar as they are brought under an equal point of view, are taken from one definite side only – for instance, in the present case, are regarded only as workers and nothing more is seen in them, everything else being ignored. Further, one worker is married, another is not; one has more children than another, and so on and so forth. Thus, with an equal performance of labor, and hence an equal in the social consumption fund, one will in fact receive more than another, one will be richer than another, and so on. To avoid all these defects, right, instead of being equal, would have to be unequal.

But these defects are inevitable in the first phase of communist society as it is when it has just emerged after prolonged birth pangs from capitalist society. Right can never be higher than the economic structure of society and its cultural development conditioned thereby.

In a higher phase of communist society, after the enslaving subordination of the individual to the division of labor, and therewith also the antithesis between mental and physical labor, has vanished; after labor has become not only a means of life but life's prime want; after the productive forces have also increased with the all-around development of the individual, and all the springs of co-operative wealth flow more abundantly – only then can the narrow horizon of bourgeois right be crossed in its entirety and society inscribe on its banners: From each according to his ability, to each according to his needs!

-Karl Marx