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

generates a code of length 57 over Z3[X]/(X^2) who´s minimum homogenous weight is 109.

Homogenous weight enumerator: w(x)=1x^0+36x^109+66x^110+240x^111+48x^112+42x^113+28x^114+48x^115+18x^117+42x^119+114x^120+24x^121+12x^122+6x^124+2x^132+2x^144

The gray image is a linear code over GF(3) with n=171, k=6 and d=109.
This code was found by Heurico 1.16 in 13.2 seconds.