An interesting problem in the field of quantum error correction involves finding a physical system that hosts a "self-correcting quantum memory," defined  as an encoded qubit  coupled to an environment that naturally wants to correct errors.  To date, a quantum memory stable against finite-temperature effects is only known in four spatial dimensions or higher. Here, we take a different approach to realize a  stable  quantum memory by relying on a driven-dissipative environment. We propose a new model which  appears to self-correct against both bit-flip and phase-flip errors in two dimensions: A square lattice composed of photonic "cat qubits" coupled  via dissipative terms which  tend to fix errors locally. Inspired by the presence of two distinct Z_2-symmetry-broken phases, our scheme relies on Ising-like dissipators to protect against bit flips and on a driven-dissipative photonic environment to protect against phase flips.