We studied a model for leptons based on the smallest modular finite group that accounts for both the hints of large low-energy CP-violation in the lepton sector and the matter-antimatter asymmetry of the Universe, generated by two heavy right-handed neutrinos through leptogenesis. These same states are also employed in a Minimal seesaw mechanism to generate light neutrino masses. The remaining particle content is the same as the Standard Model, with the only addition being a single modulus, whose vacuum expectation value is responsible for both the modular and CP-symmetry breakings. This is enough to achieve an excellent fit to low energy neutrino observables and to the required baryon asymmetry 𝜂𝐵. Various predictions for the neutrino sector observables are also provided.