We report comprehensive thermodynamic and neutron scattering measurements on the S=3/2 antiferromagnet Cs₂CoI₄, a member of the thoroughly studied family of frustrated magnets Cs₂MX₄ (M=Cu, Co, Ru, X=Br, Cl, I, O). Unlike previously studied members, Cs₂CoI₄ undergoes a structural phase transition, for which we determine the low-temperature crystallographic structure. The resulting symmetry reduction strongly affects both the magnetic exchange interactions and single-ion anisotropy. Despite the large parameter space, we propose a minimal magnetic Hamiltonian that reasonably captures the observed excitation spectrum, analyzed using extended SU(4) linear spin-wave theory.