  Quantum simulation of spin models can provide insight into complex problems
that are difficult or impossible to study with classical computers. Trapped
ions are an established platform for quantum simulation, but only systems with
fewer than 20 ions have demonstrated quantum correlations. Here we study
non-equilibrium, quantum spin dynamics arising from an engineered, homogeneous
Ising interaction in a two-dimensional array of $^9$Be$^+$ ions in a Penning
trap. We verify entanglement in the form of spin-squeezed states for up to 219
ions, directly observing 4.0$\pm$0.9 dB of spectroscopic enhancement. We also
observe evidence of non-Gaussian, over-squeezed states in the full counting
statistics. We find good agreement with ab-initio theory that includes
competition between entanglement and decoherence, laying the groundwork for
simulations of the transverse-field Ising model with variable-range
interactions, for which numerical solutions are, in general, classically
intractable.
