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.