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  0 2X  X  1  1  0 2X
 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  X  1  1  1  1  0  1  1
 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 2X X+2  X X+1 X+2 2X  1 X+1
 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 2X  X  0  0 2X 2X  0  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+138x^103+234x^104+90x^105+264x^106+234x^107+60x^108+192x^109+192x^110+10x^111+126x^112+120x^113+38x^114+114x^115+54x^116+14x^117+72x^118+78x^119+8x^120+42x^121+60x^122+12x^123+18x^124+6x^126+6x^127+4x^132

The gray image is a linear code over GF(3) with n=165, k=7 and d=103.
This code was found by Heurico 1.13 in 0.0503 seconds.