The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  X  1  1  1  X  X  1  1  1  X  X  1  X  1  3  3  0  X  X  X  X  1  1  1  1
 0  3  6  0  3  6  0  3  6  0  3  6  0  3  6  0  3  6  0  3  6  0  3  6  0  3  6  0  3  3  6  6  0  3  6  3  6  0  3  6  3  6  0  0  3  3  6  3  0  3  6  0  6  0  3  0

generates a code of length 56 over Z9[X]/(X^2+6,3X) who´s minimum homogenous weight is 112.

Homogenous weight enumerator: w(x)=1x^0+54x^112+14x^114+8x^117+2x^120+2x^126

The gray image is a code over GF(3) with n=504, k=4 and d=336.
This code was found by Heurico 1.16 in 0.0494 seconds.