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

generates a code of length 58 over Z3[X]/(X^2) who´s minimum homogenous weight is 113.

Homogenous weight enumerator: w(x)=1x^0+108x^113+36x^114+24x^117+16x^120+54x^122+2x^135+2x^147

The gray image is a linear code over GF(3) with n=174, k=5 and d=113.
This code was found by Heurico 1.16 in 0.944 seconds.