Here, we report on synthesis and characterization of single crystals of the hexagonal Ga-containing κ-carbide phase Mo3(2+y)Ga3(1-x)Fe1+3(1-y+x)C4 with x = 0.15, y = 0.35 and mixed occupation of two 6 h sites. We refined its crystal structure as hexagonal with P63/mmc symmetry. We combined polarized Raman spectroscopy, X-ray absorption near edge structure, X-ray magnetic circular dichroism and electrical resistivity measurements with density functional theory in order to give a first consistent description of the structural, electronic and magnetic properties of this new compound. The phase exhibits metallic conductivity, has a high thermal stability in inert atmosphere and surprisingly has a non-magnetic ground state. Our study provides further impetus for the rediscovery of the κ-phase family, which, due to its chemical diversity, should have many physical properties to be easily tailored. Display omitted