The generator matrix

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

generates a code of length 55 over Z3[X]/(X^2) who´s minimum homogenous weight is 93.

Homogenous weight enumerator: w(x)=1x^0+194x^93+492x^94+768x^95+1112x^96+1686x^97+1824x^98+2604x^99+3558x^100+3636x^101+5022x^102+6270x^103+5670x^104+7452x^105+9660x^106+8412x^107+10306x^108+12252x^109+10182x^110+11502x^111+12330x^112+9684x^113+9890x^114+10518x^115+6984x^116+6608x^117+5766x^118+3570x^119+3130x^120+2292x^121+1422x^122+970x^123+600x^124+276x^125+214x^126+186x^127+54x^128+20x^129+6x^131+12x^132+2x^135+2x^138+4x^141+2x^144+2x^147

The gray image is a linear code over GF(3) with n=165, k=11 and d=93.
This code was found by Heurico 1.16 in 412 seconds.