In this Letter we present a discrete modulated, continuous variables quantum key distribution implementation using two probabilistically shaped, 128-symbol, amplitude and phase shift keying constellations. At Bob's detection side, a polarization diverse, true heterodyne receiver architecture is implemented for symbol recovery. We demonstrate experimentally that our system is capable of achieving security against collective attacks, while using accessible, telecom-grade material, and of functioning for an indefinitely long period of time at distances in excess of 185 km, in the asymptotic regime.