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

generates a code of length 55 over Z3[X]/(X^3) who´s minimum homogenous weight is 103.

Homogenous weight enumerator: w(x)=1x^0+156x^103+258x^104+68x^105+372x^106+168x^107+860x^108+606x^109+1176x^110+1664x^111+558x^112+180x^113+56x^114+66x^115+66x^116+12x^117+114x^118+30x^119+8x^120+60x^121+48x^122+2x^123+12x^124+18x^125+2x^156

The gray image is a linear code over GF(3) with n=495, k=8 and d=309.
This code was found by Heurico 1.16 in 3.48 seconds.