Here we perform a steady state thermodynamic analysis of a cogeneration cycle capable of producing power through a supercritical Carbon Dioxide (sCO2) recompression Brayton cycle and water through a Multi Effect Distillation (MED) plant. The integration considers a demineralized water loop heated by rejected sCO2. Thus, the performance of the power block is independent of the desalination block. Each block of the system is independently analyzed to identify the operational or design parameters that influence the thermodynamic efficiency and water and power production. For a power block producing 112.6 MW, with a fixed turbine inlet temperature, the pressure ratio (PR) is the most influential variable in order to maximize net power production and thermal efficiency. For the desalination block, producing 2659 m3/d of water, the last effect temperature (TN) is the most influential variable for water production. In the integrated cogeneration system, increasing PR beyond the power block optimized value (From PR = 3.5 to 3.96) reduces power (from 112.6 to 112.4 MW), but increases water production (from 35 to 40 kg/s), and decreases the specific energy consumption from 29.4 kWh/m3 of water to 26.5 kWh/m3 of water.