  A code algebra $A_C$ is a nonassociative commutative algebra defined via a
binary linear code $C$. In a previous paper, we classified when code algebras
are $\mathbb{Z}_2$-graded axial (decomposition) algebras generated by small
idempotents. In this paper, for each algebra in our classification, we obtain
the Miyamoto group associated to the grading. We also show that the code
algebra structure can be recovered from the axial decomposition algebra
structure.
