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

generates a code of length 64 over Z9[X]/(X^2+3,3X) who´s minimum homogenous weight is 123.

Homogenous weight enumerator: w(x)=1x^0+54x^123+48x^124+160x^126+60x^127+1620x^128+104x^129+18x^130+42x^132+24x^133+34x^135+12x^136+8x^138+2x^192

The gray image is a code over GF(3) with n=576, k=7 and d=369.
This code was found by Heurico 1.16 in 0.139 seconds.