Extend the HexagonTile or create new Hexagon2Tile to create the $XYZ^2$ hexagonal code

[dsvandet]

What is the expected enhancement?

The $XYZ^2$ code, see XYZ2 Code, can be created from the HexagonTile if the option to include weight two operators on any of the sides (a set of sides is needed for the $XYZ^2$ code).

The current Tile has:

                          q0      q1
                          v0      v1
                           o-----o
                      q3  /       \  q4
                      v5 o    0    o v2
        q2      q3        \       /
        v0      v1      q6 o-----o q7
         o-----o        v4         v3
    q5  /       \  q6  .(0,0)
    v5 o    1    o v2    q6       q7
        \       /        v0       v1
         o-----o           o-----o
        v4      v3    q9  /       \ q10
        q8      q9    v5 o    2    o v2
                          \       /
                           o-----o
                         v4       v3
                        q11       q12

In the new tile we are adding the option to include any of the nine weight 2 stabilizers A,B,C,...,H given in the image below that are colored in pink. So for the $XYZ^2$ hexagon code we would turn on the three weight two stabilizers B, I, and G as Pauli('XX') operators.

So the option is to modify the existing tile or create a new one. Pros and Cons of both solutions as there are other modifications/additions that can be made.

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