  Error correcting codes protect quantum information and form the basis of
fault tolerant quantum computing. Leading proposals for fault-tolerant quantum
computation require codes with an exceedingly rare property, a transverse
non-Clifford gate. Codes with the desired property are presented for $d$-level,
qudit, systems with prime $d$. The codes use $n=d-1$ qudits and can detect upto
$\sim d/3$ errors. We quantify the performance of these codes for one approach
to quantum computation, known as magic state distillation. Unlike prior work,
we find performance is always enhanced by increasing $d$.
