We investigate the performance of a self-homodyne coherent detection (SHCD) system using a 19 core multi-core fiber (MCF) and 16 wavelength-division-multiplexed channels. We show that SHCD, with the pilot-tone transmitted on a single MCF core and information carrying signals on the remaining cores, is compatible with space-division-multiplexed transmission, potentially relaxing laser linewidth and digital signal processing requirements due to phase noise cancellation. However, inter-core crosstalk can have an impact on performance and core selection.