Materials in the Na-rich antiperovskite family are promising candidates as solid electrolytes (SEs) for all-solid-state Na-ion batteries (NIBs). In this work, we carry out ab-initio calculations to study various properties of Na3OCI, namely the formation energies of various neutral defect pairs, the defect hopping barriers, the solution energies of high valence alkali earth metal substitutes to the Na atoms, and the effect of such substitution to the Na migration. While the introduction of alkali earth metal ions increases the Na vacancy concentration, the activation energy of Na transport also increases. Furthermore, we identify Ca as the most promising alkali earth metal to be doped into Na3OCl due to its low binding energy and relatively small impact on the migration barrier. Our work provides a theoretical framework for further improving the Na conductivity of materials in the antiperovskite family for all-solid-state NIBs.