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We present a quantum simulation strategy for a (1+1)D SU(2) non-abelian lattice gauge theory, a hardcore-gluon Hamiltonian Yang-Mills, tailored to a six-level trapped-ion qudit quantum processor, as recently experimentally realized. We employ a qudit encoding fulfilling gauge invariance, an SU(2) Gauss' law. We discuss the experimental feasibility of generalized M{\o}lmer-S{\o}rensen gates used to efficiently simulate the dynamics. We illustrate how a shallow circuit with these resources is sufficient to implement scalable digital quantum simulation of the model. We also numerically show that this model, albeit simple, can dynamically manifest physically-relevant properties specific to non-abelian field theories, such as baryon excitations.