The generator matrix
1 0 1 1 1 1 1 0 1 0 1 1 1 1 1 0 X 1 1 1 0 1 1 1 1 1 X 1 1 1 1 1 1 1 1 2X 1 1 0 1 1 1 1 1 0 1 2X 1 X 1 1 1 1 1 1 1 1 0
0 1 1 2 0 1 2 1 2X+1 1 0 2 X+2 2X+1 0 1 1 0 2 X+1 1 0 2 2X+1 X+1 2 1 2X+2 X 2X+1 2X+2 2X+1 X X 1 1 2X+2 2X+1 1 2X+1 X+2 2X+2 X+2 1 1 2X 1 1 1 2X 1 X+1 0 X 2X+2 X+2 X+2 1
0 0 2X 0 0 0 0 0 0 0 2X X X 2X 2X 2X 2X 2X 2X X 0 X X 2X 0 X X X X X X X X 0 2X X 0 X X X 2X 2X 2X 2X 2X X 2X X 2X X 2X 2X 2X X 2X 0 X 2X
0 0 0 X 0 0 0 X 2X X 0 2X X 2X 2X 0 2X 2X 0 2X 2X 2X 2X X X X 2X 0 X X 2X 0 2X 2X 0 2X X 2X 2X X 2X 2X 2X 0 0 0 X 2X X 0 X 0 2X 0 2X X X 0
0 0 0 0 X 0 X X X X X 2X 0 X X 0 2X 0 0 X X 2X 0 X 0 2X 2X X 2X X 0 0 X 0 2X X X 2X X 0 0 X 2X 2X X 2X 2X X X X X 0 X X X X X 2X
0 0 0 0 0 2X 2X 0 2X X 0 2X X X 2X 2X X X 2X 0 X X 0 0 2X 0 X 2X X 0 X 0 2X X 0 X X 2X 0 2X 2X 2X 2X 2X X 0 2X X 0 X X 2X 0 0 X X 0 X
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+330x^105+756x^108+726x^111+1262x^114+1264x^117+1020x^120+818x^123+250x^126+36x^129+54x^132+20x^135+16x^141+2x^144+4x^150+2x^153
The gray image is a linear code over GF(3) with n=174, k=8 and d=105.
This code was found by Heurico 1.16 in 8.97 seconds.