High-gradient CW photo-injectors operating at high accelerating gradients promise to revolutionize many sciences and applications. They can establish the basis for super-bright monochromatic X-ray free-electron lasers, super-bright hadron beams, nuclear- waste transmutation or a new generation of microchip production. In this letter we report on our operation of a superconducting RF electron gun with a record-high accelerating gradient at the CsK2Sb photocathode (i.e. ~ 20 MV/m) generating a record-high bunch charge (i.e., 3 nC). We briefly describe the system and then detail our experimental results. This achievement opens new era in generating high-power electron beams with a very high brightness.