New cuprates with the nominal composition $(Pb_{0.75}Sn_{0.25})Sr_2(Ca_{1-x}Lu_x)Cu_2O_z(x=0.4{sim}1.0)$ have been synthesized. These materials exhibit superconducting properties for 0.4 $leq$ x $leq$ 0.7. It is also observed that the superconductivity of the as-prepared sample is enhanced by post-annealing at high temperature followed by quenching. X-ray diffraction analysis reveals that the c lattice parameter decreases as x increases whereas the a lattice parameter is nearly independent of the value of x for both the as-prepared and the post-treated samples. The thermoelectric power measurements indicate that the post-heat-treatments result in an increase in the hole carrier density which account for the observed increase of $T_c$. Bulk superconductivity with a $T_c$ value of 60 K is observed in this system.