The generator matrix

 1  0  0  1  1  1  1  X  1  1 2X  1  1  1  0  1  1  1  X  0  1  1  1  1  1  X  1  0  1  1  1 2X  1  1  1  1  1  1  1  1 2X  1  0  1  0  1  1  1  1  1 2X  0  1  1  1  1  1
 0  1  0  0  0 2X+1  1  1 2X+2 2X+1  1  2  2 2X  X 2X X+2  X  1  1  1 2X+1 2X+2  1 2X+2  1  2  1 2X+1  X 2X+1  X 2X X+1 2X X+2  1 X+2  2  1  1  0  0  0  1  2 X+2  X X+1 2X+1  1  1 2X 2X+2 2X+2  X X+1
 0  0  1  1  2 2X+2  1 X+2 2X+1 2X  1  0 X+2  X  1 X+2  1 2X+1  2 X+1  X X+2  X X+1  2  1 2X+2  0  X  2 2X+2  1 2X+1 X+2  0  2 X+2 2X+1 2X+2 2X  2 X+2  1 2X+2 2X+2 X+1 X+1 2X+2  1  1  1 X+1  X  0 2X 2X+1  X
 0  0  0 2X  0  0  0  0  0 2X  X  X 2X 2X 2X  X  0  0 2X  0  X  X  0 2X  X  X  0  X 2X  0 2X  0  X 2X  0 2X  X 2X  0 2X  0 2X  X 2X 2X  X  X 2X  0  X 2X 2X 2X  0 2X  0  0
 0  0  0  0  X  X  X  0  X  0  X  0 2X  0 2X  0  0 2X  X 2X 2X 2X 2X  0  0 2X  0 2X  X  0 2X  X  X  X 2X  X  X 2X 2X 2X 2X  X  0 2X 2X 2X  0  0  0  X 2X  0  X  X 2X  X 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+658x^105+1144x^108+1074x^111+1146x^114+934x^117+810x^120+470x^123+232x^126+78x^129+10x^132+2x^135+2x^141

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 6.85 seconds.