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

generates a code of length 58 over Z3[X]/(X^2) who´s minimum homogenous weight is 108.

Homogenous weight enumerator: w(x)=1x^0+30x^108+72x^110+54x^111+72x^113+56x^114+162x^116+38x^117+144x^119+28x^120+36x^122+8x^123+6x^126+6x^129+6x^132+2x^141+6x^144+2x^156

The gray image is a linear code over GF(3) with n=174, k=6 and d=108.
This code was found by Heurico 1.16 in 0.0336 seconds.