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  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  X
 0  X 2X  0 X+6 2X X+6 2X+3  0  3  0  3 X+6 2X  3 X+6 X+3 2X+3  X  3  X  6  X 2X 2X+3 2X+3 2X+6  0  0  3  3 X+6 X+6 X+3  X  X  0  6  X 2X 2X+3 2X 2X+3 2X 2X+6  3 X+3 2X+3  6 2X+6 2X 2X+6 X+6 2X+6 X+6 X+6
 0  0  3  0  3  0  6  6  3  6  3  6  6  0  0  3  0  3  3  3  6  6  0  3  6  0  6  0  3  3  0  6  3  0  0  3  6  0  6  6  0  6  3  6  3  3  6  0  0  6  0  3  0  0  6  3
 0  0  0  3  6  3  3  6  6  3  0  6  6  0  6  0  6  3  3  3  0  0  3  6  3  6  0  6  3  0  0  0  3  0  6  0  0  3  6  6  3  3  6  0  0  6  3  0  0  6  6  3  0  3  3  6

generates a code of length 56 over Z9[X]/(X^2+6,3X) who´s minimum homogenous weight is 108.

Homogenous weight enumerator: w(x)=1x^0+282x^108+420x^111+972x^112+378x^114+84x^117+48x^120+2x^162

The gray image is a code over GF(3) with n=504, k=7 and d=324.
This code was found by Heurico 1.16 in 0.156 seconds.