The generator matrix

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

generates a code of length 58 over Z3[X]/(X^2) who´s minimum homogenous weight is 105.

Homogenous weight enumerator: w(x)=1x^0+132x^105+136x^108+144x^111+626x^114+636x^117+288x^120+96x^123+36x^126+48x^132+20x^135+16x^141+6x^144+2x^162

The gray image is a linear code over GF(3) with n=174, k=7 and d=105.
This code was found by Heurico 1.16 in 0.794 seconds.