We have determined the crystal structures and superconducting transition temperatures of La1.48Nd0.4Sr0.12CuO4 under nearly hydrostatic pressures in diamond anvil cells to 5.0 GPa and 19.0 GPa, respectively. Synchrotron x-ray powder diffraction measurements were used to establish the pressure-temperature structural phase diagram. Under pressure the superconducting transition temperature increases rapidly from Tc = 3 K to a maximum value of 22 K at 5 GPa, a pressure slightly greater than that required to stabilize the undistorted I4/mmm structure in the superconducting state. Increasing the pressure further to 19 GPa leads to a decrease in Tc to ~12 K. These results are discussed in relation to earlier high pressure measurements for similar materials.