In what type of society did Karl Marx expect to see social stratification based on greed?

Marx expected to see social stratification based on greed in capitalist society. One of the principles of Marx and Engel's work was that economics determine how a society is structured. In other words, whatever personal traits yield wealth for the society as a whole are the traits that will be most valued and honored. Therefore, a society that derived most of its wealth from its ability to hunt and kill large animals would most value the traits of physical strength and bravery, because those traits would enable successful hunting. The people who exhibited those traits would be on the top of the social heap in that culture. In a society where, on the other hand, most of the wealth derived from agriculture, people who owned the land and managed it in a stable way would be most valued and at the top of the social strata.
In capitalist culture, wealth is said to derive from those who own the most capital (roughly speaking, money). If physical strength and bravery were the traits that would make a person the most successful hunter, greed is the trait that makes the most successful capitalist. Therefore, greed would catapult people to the top in capitalist society.
It is worth nothing that Marx thought the idea that capital created wealth was a lie, what he called a mystification, and he asserted that in reality, labor creates all wealth, a concept still being debated.