  We apply the recent graphical framework of ''quantum lego'' to XP stabilizer
codes where the stabilizer group is generally non-abelian. We show that the
idea of operator matching continues to hold for such codes and is sufficient
for generating all their XP symmetries provided the resulting code is XP. We
provide an efficient classical algorithm for tracking these symmetries under
tensor contraction or conjoining. This constitutes a partial extension of the
algorithm implied by Gottesman-Knill theorem beyond Pauli stabilizer states and
Clifford operations. Because conjoining transformations generate quantum
operations that are universal, the XP symmetries obtained from these algorithms
do not uniquely identify the resulting tensors in general. Using this extended
framework, we provide a novel XP stabilizer code with higher distance and a
$[[8,1,2]]$ code with fault-tolerant $T$ gate. For XP regular codes, we also
construct a tensor-network-based the maximum likelihood decoder for any i.i.d.
single qubit error channel.
