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

generates a code of length 58 over Z3[X]/(X^2) who´s minimum homogenous weight is 111.

Homogenous weight enumerator: w(x)=1x^0+122x^111+270x^114+158x^117+92x^120+72x^123+8x^126+4x^135+2x^156

The gray image is a linear code over GF(3) with n=174, k=6 and d=111.
This code was found by Heurico 1.16 in 0.285 seconds.