  Most known quantum codes are additive, meaning the codespace can be described
as the simultaneous eigenspace of an abelian subgroup of the Pauli group. While
in some scenarios such codes are strictly suboptimal, very little is understood
about how to construct nonadditive codes with good performance. Here we present
a family of nonadditive quantum codes for all odd blocklengths, n, that has a
particularly simple form. Our codes correct single qubit erasures while
encoding a higher dimensional space than is possible with an additive code or,
for n of 11 or greater, any previous codes.
