The generator matrix

1 0 0 0 1 1 1 0 1 1 1 1 0 0 0 0 1 1 X X X 1 1 1 X 1 X 1 1 1 1 X X X X X 0 0 0 1 1 X 0 X 1 X 1 X 1 1 0 1 1 0 X 0 0 1
0 1 0 0 0 0 0 X 1 1 1 1 1 1 1 0 X X 1 0 1 X X 0 1 0 1 X+1 X+1 X+1 X+1 1 0 1 X 0 1 1 X X X+1 X 1 1 X 0 1 X 1 X+1 0 X+1 1 X 0 X 0 0
0 0 1 0 1 X X+1 1 0 X+1 1 X 1 X X+1 1 0 1 0 0 X X+1 X 1 1 0 X+1 0 X+1 X 1 X+1 1 0 1 1 0 1 1 X 0 1 1 X+1 0 1 X X X X X X 0 X 1 0 1 0
0 0 0 1 X 1 X+1 1 X+1 0 1 X X 1 X+1 X+1 1 0 X 1 1 X X+1 X+1 X X 0 X+1 1 0 X 1 X X+1 1 1 1 0 X X 1 X+1 X+1 X+1 X+1 0 1 1 X+1 1 1 X+1 1 1 X+1 1 0 0

generates a code of length 58 over Z2[X]/(X^2) who´s minimum homogenous weight is 54.

Homogenous weight enumerator: w(x)=1x^0+22x^54+36x^55+48x^56+56x^57+16x^58+16x^59+16x^60+5x^62+12x^63+9x^64+4x^65+1x^66+4x^68+1x^70+2x^72+4x^73+3x^74

The gray image is a linear code over GF(2) with n=116, k=8 and d=54.
This code was found by Heurico 1.10 in 0 seconds.