  The quantum simulation of dynamical gauge field theories offers the
opportunity to study complex high-energy physics with controllable low-energy
devices. For quantum computation, bosonic codes promise robust error correction
that exploits multi-particle redundancy in bosons. Here, we demonstrate how
bosonic codes can be used to simulate dynamical gauge fields. We encode both
matter and dynamical gauge fields in a network of resonators that are coupled
via three-wave-mixing. The mapping to a $\mathbb{Z}_2$ dynamical lattice gauge
theory is established when the gauge resonators operate as Schr\"odinger cat
states. We explore the optimal conditions under which the system preserves the
required gauge symmetries. Our findings promote realising high-energy models
using bosonic codes.
