The generator matrix

 1  0  0  1  1  1  X  1  1  X  1  0  0  1  1  1  0  1  1  0  1  1  0  0  1  1  0  0  X  X  X  X  0  X  X  0  1  1  1  0  1  X  1  1  0  1  1  X  X  X  0  1  1  X  0  X  1  1
 0  1  0  0  1 X+1  1  0  1  1 X+1  1  0  0  X X+1  1  X X+1  1  X  1  1  X  X  1  1  X  1  1  1  1  1  1  1  1  0  0 X+1  1 X+1  1  X  1  1  X  1  1  0  0  X  X  X  1  1  1  0  X
 0  0  1  1  1  0  1  X X+1 X+1  X  X  1 X+1  X X+1 X+1  0  1  1  1  X  0  1 X+1  0  X  1  1  1  1 X+1 X+1 X+1 X+1  1  0  0  0  X  0  X  0  0  X  0  0  X  X  X  X  1 X+1  X  0  0 X+1 X+1
 0  0  0  X  0  0  0  0  0  0  0  0  0  X  X  X  X  X  X  X  0  X  X  X  0  X  X  X  0  X  X  0  0  X  X  0  0  X  0  X  X  0  X  X  0  0  0  X  X  0  0  0  X  0  X  X  X  X
 0  0  0  0  X  X  0  X  0  X  0  X  X  X  X  0  0  0  X  X  0  0  0  0  X  X  X  X  X  0  X  0  X  0  X  0  X  X  0  0  0  0  X  0  0  X  0  0  X  X  X  X  0  X  X  0  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+20x^54+52x^55+46x^56+24x^57+23x^58+32x^59+8x^60+8x^61+15x^62+4x^63+7x^64+4x^70+8x^71+2x^72+1x^74+1x^78

The gray image is a linear code over GF(2) with n=116, k=8 and d=54.
This code was found by Heurico 1.16 in 0.047 seconds.