  We introduce a morphing procedure that can be used to generate new quantum
codes from existing quantum codes. In particular, we morph the 15-qubit
Reed-Muller code to obtain a $[\![10,1,2]\!]$ code that is the smallest known
stabilizer code with a fault-tolerant logical $T$ gate. In addition, we
construct a family of hybrid color-toric codes by morphing the color code. Our
code family inherits the fault-tolerant gates of the original color code,
implemented via constant-depth local unitaries. As a special case of this
construction, we obtain toric codes with fault-tolerant multi-qubit control-$Z$
gates. We also provide an efficient decoding algorithm for hybrid color-toric
codes in two dimensions, and numerically benchmark its performance for
phase-flip noise. We expect that morphing may also be a useful technique for
modifying other code families such as triorthogonal codes.
