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

generates a code of length 57 over Z9[X]/(X^2+6,3X) who´s minimum homogenous weight is 108.

Homogenous weight enumerator: w(x)=1x^0+46x^108+60x^110+128x^111+216x^112+36x^113+1076x^114+432x^115+36x^116+44x^117+12x^119+64x^120+18x^122+14x^123+2x^126+2x^168

The gray image is a code over GF(3) with n=513, k=7 and d=324.
This code was found by Heurico 1.16 in 0.0962 seconds.