The exploitation of the full structure of multimode light fields enables compelling capabilities in many fields including classical and quantum information science. We exploit data-encoding on the optical phase of the pulses of a femtosecond laser source for a photonic implementation of a reservoir computing protocol. Rather than intensity detection, data-reading is done via homodyne detection that accesses combinations of an amplitude and a phase of the field. Numerical and experimental results on nonlinear autoregressive moving average (NARMA) tasks and laser dynamic predictions are shown. We discuss perspectives for quantum-enhanced protocols.