The generator matrix

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

generates a code of length 55 over Z3[X]/(X^2) who´s minimum homogenous weight is 105.

Homogenous weight enumerator: w(x)=1x^0+112x^105+278x^108+180x^111+66x^114+84x^117+6x^126+2x^159

The gray image is a linear code over GF(3) with n=165, k=6 and d=105.
This code was found by Heurico 1.16 in 0.0336 seconds.