Using first-principles calculations based on density functional theory, we probe the electronic and magnetic properties of X2PtGa (X being Cr, Mn, Fe, Co) Heusler alloys. Our calculations predict that all these systems possess inverse Heusler alloy structure in the respective ground states. Application of tetragonal distortion leads to lowering of energy with respect to their cubic phase. The equilibrium volumes of both the phases are nearly the same. These indicate that the materials studied here are prone to undergo martensite transition, as has been recently shown theoretically for Mn2PtGa in the literature. Ground state with a tetragonal symmetry is corroborated by the observation of soft tetragonal shear constants in the cubic phase. By comparing the energies of various types of magnetic configurations we predict that Cr2PtGa and Mn2PtGa possess ferrimagnetic configuration whereas Fe2PtGa and Co2PtGa possess ferromagnetic configuration in their respective ground states.