The generator matrix

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

generates a code of length 55 over Z3[X]/(X^2) who´s minimum homogenous weight is 103.

Homogenous weight enumerator: w(x)=1x^0+192x^103+204x^104+62x^105+210x^106+258x^107+58x^108+222x^109+192x^110+50x^111+102x^112+144x^113+28x^114+54x^115+60x^116+36x^117+96x^118+72x^119+4x^120+66x^121+30x^122+24x^124+6x^125+2x^126+6x^127+6x^128+2x^135

The gray image is a linear code over GF(3) with n=165, k=7 and d=103.
This code was found by Heurico 1.16 in 0.242 seconds.