In this article we define an encoding for parabolic permutations that distin-guishes between parabolic 231-avoiding permutations. We prove that the compo-nentwise order on these codes realizes the parabolic Tamari lattice, and conclude a direct and simple proof that the parabolic Tamari lattice is isomorphic to a certain ν-Tamari lattice, with an explicit bijection. Furthermore, we prove that this bijec-tion is closely related to the map Θ used when the lattice isomorphism was first proved in (Ceballos, Fang and Mühle, 2020), settling an open problem therein.