  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).
