The system of property includes the mechanisms that enforce property rights, which, in the case of cryptocurrencies, does include their code.
However, established property systems (courts, police, etc.) acknowledge only human property owners, or corporations which must in turn be owned by something else, eventually leading to a human. Even cryptocurrencies, which can theoretically be owned by anything with a private key, are in practice owned by humans — because most people don’t want to gather a bunch of BTC and then give it to a computer they don’t control.
Someone might design a computer to manage money for them, but they are generally going to retain ownership of the money, and give themselves a means of controlling their computer.
Property ownership is fundamentally different from work: work is difficult and dull and people don’t like doing unless they can get paid. Property ownership gives the owner great benefit with little effort, so no one is going to design a robot to own their property for them (barring a few possible utopian ideas).