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 2X^2  1  X  0  1  1  1  1  1
 0  X  0  0  0 2X 2X^2+X 2X^2+2X  X 2X^2+2X 2X^2 2X^2 2X^2+X 2X^2+2X 2X 2X^2+X 2X^2+X 2X^2+X 2X^2+2X X^2+X X^2+X  0 2X 2X^2+2X 2X^2+2X X^2  0 2X 2X  X 2X^2+X  X 2X^2  0 X^2 2X^2 2X^2+X X^2+X  X X^2 X^2+2X X^2 2X^2+2X 2X^2+2X  0 2X^2 2X^2+2X  X 2X X^2+X  X 2X^2+X 2X^2+X 2X  X  0
 0  0  X  0 X^2 2X^2 X^2 2X^2  0  0 2X^2+X X^2+2X X^2+2X 2X^2+2X X^2+X  X 2X  X X^2+2X  X X^2+2X X^2+2X 2X^2+X 2X^2+X 2X^2+2X  X X^2+2X 2X^2 X^2+2X 2X^2 2X^2+2X X^2+2X X^2+X 2X  X 2X^2 2X^2+X 2X^2+X 2X^2+2X  0 2X X^2+2X X^2 2X 2X^2+X 2X^2 2X^2+2X  0 2X^2+X X^2+X  0 2X 2X^2  0 2X^2+2X 2X^2
 0  0  0  X 2X^2+2X  0 2X X^2+X  X 2X 2X^2+2X X^2 2X^2  0 X^2 X^2+X X^2+X 2X^2 X^2+2X 2X X^2+2X 2X 2X X^2+X  X  X X^2+X  X 2X 2X^2+X  X X^2+2X 2X^2+X  X X^2+2X 2X^2 2X  0  X 2X X^2+X  0 X^2+X  X 2X^2 2X^2+X 2X^2 X^2+X X^2+2X X^2+2X 2X^2+X 2X^2  0 2X^2+X X^2  0

generates a code of length 56 over Z3[X]/(X^3) 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 linear code over GF(3) with n=504, k=9 and d=306.
This code was found by Heurico 1.16 in 1.68 seconds.