The generator matrix

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

generates a code of length 57 over Z3[X]/(X^2) who´s minimum homogenous weight is 105.

Homogenous weight enumerator: w(x)=1x^0+546x^105+1190x^108+1248x^111+1176x^114+900x^117+618x^120+516x^123+234x^126+114x^129+12x^132+6x^135

The gray image is a linear code over GF(3) with n=171, k=8 and d=105.
This code was found by Heurico 1.16 in 0.547 seconds.