Qutrit codes within representations of SU(3)

We describe a quantum error-detecting and error-correcting code embedded within irreducible representations of SU(3). These logical qutrits inherit the He(3) symmetries induced by the representation, while protecting against small SU(3) displacements. We explore the general methodology for finding codes from structure-inducing representations of groups, together with symmetries inherited from finite subgroups, extending the case of spin representations of SU(2).