  We construct a family of infinitely many new candidate non-Abelian
self-correcting topological quantum memories in $D\geq 5+1$ spacetime
dimensions without particle excitations using local commuting non-Pauli
stabilizer lattice models and field theories of $\mathbb{Z}_2^3$ higher-form
gauge fields with nontrivial topological action. We call such non-Pauli
stabilizer models magic stabilizer codes. The family of topological orders have
Abelian electric excitations and non-Abelian magnetic excitations that obey
Ising-like fusion rules, generalizing the dihedral group $\mathbb{D}_8$ gauge
theory in 2+1d. The simplest example includes a new non-Abelian self-correcting
memory in 5+1d with Abelian loop excitations and non-Abelian membrane
excitations. We use a Peierls argument to demonstrate the self-correction
property and the thermal stability, and devise a probablistic local
cellular-automaton decoder.
