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  X  X  0  1  1  1  1  X  X  0  1  1  1  X  X  3  1  1  1  1  1  1  X  1  1  1  1  X  X
 0  X 2X  0 X+6 2X  3 X+6 2X+3  3 X+3 2X+3  3 X+3 2X  0  X 2X+3  6  6 X+6 X+3 2X+6 2X+6  6  X 2X+6 X+6 2X  X  0 X+6 2X  0 X+6 2X  X  3 X+6 X+3 X+3 2X+3  X  3 X+3  3  0 X+6 X+3  6 2X+3 2X+6 2X 2X+6 X+3 2X+3
 0  0  3  3  6  6  6  3  0  3  0  3  0  3  0  6  6  6  0  3  0  6  3  6  6  3  0  6  0  3  0  6  0  6  3  3  0  3  3  0  0  6  6  6  6  0  3  0  3  3  6  3  3  0  3  0

generates a code of length 56 over Z9[X]/(X^2+6,3X) who´s minimum homogenous weight is 109.

Homogenous weight enumerator: w(x)=1x^0+96x^109+240x^110+8x^111+78x^112+108x^113+8x^114+96x^115+72x^116+2x^117+12x^119+4x^120+2x^123+2x^132

The gray image is a code over GF(3) with n=504, k=6 and d=327.
This code was found by Heurico 1.16 in 0.0693 seconds.