Which codes can implement transversal non-Clifford gates

A paper Three-dimensional surface codes: Transversal gates and fault-tolerant architectures discusses 3D surface codes and shows that

CZ and CCZ gates are transversal in [these] codes.

They give a small example in Appendix A.
I’m a bit confused by some of the parameters. There are three codes listed there; each is $[[12,1,2]]$.

So does that mean that the "overall code" acts on 36 qubits? In that case how are the three codes
"stitched" together to form the bigger code? Alternatively, if I have some $[[n,k,d]]$ code, how do
I check if it can implement a CZ,CCZ,CCCZ,…gate or not?