  We introduce our new cosmological simulation dataset CROCODILE, executed
using the GADGET4-Osaka smoothed particle hydrodynamics code. This simulation
incorporates an updated supernova (SN) feedback model of Oku et al. (2022) 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 IMF, which enables a higher energy injection rate per unit stellar
mass formed at high redshift. The CROCODILE dataset 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 the SN feedback is a key driver in the chemical
enrichment of the IGM. Additionally, the AGN feedback creates metal-rich,
bipolar outflows that extend and enrich the CGM and IGM over a few Mpc scales.
