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

generates a code of length 56 over Z9[X]/(X^2+3,3X) who´s minimum homogenous weight is 102.

Homogenous weight enumerator: w(x)=1x^0+134x^102+240x^103+324x^104+232x^105+624x^106+708x^107+784x^108+1020x^109+1836x^110+2244x^111+2976x^112+2742x^113+2110x^114+1362x^115+732x^116+256x^117+276x^118+252x^119+206x^120+192x^121+138x^122+82x^123+84x^124+54x^125+24x^126+18x^127+18x^128+12x^130+2x^147

The gray image is a code over GF(3) with n=504, k=9 and d=306.
This code was found by Heurico 1.16 in 1.89 seconds.