We have developed a high-throughput computational method to predict the superconducting transition temperature in stable hexagonal M2AX phases and applied it to all the known possible choices for M (M: Sc, Ti, V, Cr, Mn, Fe, Y, Zr, Nb, Mo, Lu, Hf and Ta). We combine this with the best candidates for A (A: Al, Cu, Ge and Sn) and X (X: C and N) from our previous work, and predict Tc for 60 M2AX-phase materials, 53 of which have never been studied before. From all of these, we identify Cr2AlN as the best candidate for the highest Tc, and confirm its high Tc with more detailed density functional theory electron-phonon coupling calculations. Our detailed calculations predict Tc = 14.8 K for Cr2AlN, which is significantly higher than any Tc value known or predicted for any material in the M2AX family to date.