We introduce our new cosmological simulation data set CROCODILE, executed using the GADGET4-Osaka smoothed particle hydrodynamics code. This simulation incorporates an updated supernova (SN) feedback model of Y. Oku et al. and an active galactic nuclei (AGN) feedback model. A key innovation in our SN feedback model is the integration of a metallicity- and redshift-dependent, top-heavy initial mass function. Our SN model introduces a new consideration that results in an order of magnitude difference in the energy injection rate per unit stellar mass formed at high redshift. The CROCODILE data set is comprehensive, encompassing a variety of runs with diverse feedback parameters. This allows for an in-depth exploration of the relative impacts of different feedback processes in galactic evolution. Our initial comparisons with observational data, spanning the galaxy stellar mass function, the star formation main sequence, and the mass–metallicity relation, show promising agreement, especially for the Fiducial run. These results establish a solid foundation for our future work. We find that SN feedback is a key driver in the chemical enrichment of the intergalactic medium (IGM). Additionally, the AGN feedback creates metal-rich, bipolar outflows that extend and enrich the circumgalactic medium and IGM over a few Mpc scales.