The generator matrix
1 0 1 1 1 0 1 1 0 1 1 0 X 1 1 1 1 0 1 X 1 1 1 0 1 1 0 X 1 1 0 1 1 1 1 X 1 1 1 1 X 1 0 1 0 1 1 1 X 1 1 1 1 1 1 0 1 1
0 1 1 0 1 1 0 1 1 X X+1 1 1 0 X+1 0 X+1 1 X+1 1 X 0 X+1 1 X+1 0 1 1 0 X+1 1 X+1 0 0 X 1 X X+1 X+1 0 1 X 1 X 1 1 1 1 1 0 0 1 1 X 1 1 X 0
0 0 X 0 0 0 0 0 0 0 X 0 0 X X X X 0 0 0 0 X X X X 0 0 X X X X 0 0 X 0 X 0 X 0 X X 0 0 X X X 0 0 X X X X 0 X 0 0 X 0
0 0 0 X 0 0 0 0 0 X 0 0 0 0 X X 0 X X X X X X X X 0 X 0 X 0 0 X 0 X 0 X X X X 0 0 X X X X X 0 X 0 0 0 X X X 0 X 0 0
0 0 0 0 X 0 0 0 0 0 X X X X 0 X X X X X 0 X X X 0 X 0 X X 0 X X X X X 0 X X X X X 0 0 0 X 0 X X X 0 X 0 0 0 0 X X 0
0 0 0 0 0 X 0 0 X 0 0 X 0 X 0 X 0 X 0 0 0 X X X X 0 X X 0 X 0 X 0 0 X X X 0 X 0 X X 0 0 X 0 X 0 0 X 0 0 0 X 0 0 X X
0 0 0 0 0 0 X 0 X X 0 0 X X 0 0 X 0 X 0 X X X X 0 0 0 X 0 X X 0 X X 0 X 0 0 X 0 0 X X 0 0 X 0 0 X 0 0 X X X X 0 0 0
0 0 0 0 0 0 0 X X 0 X 0 X X X 0 0 X 0 X X X 0 X X X 0 X 0 X 0 0 X X 0 0 X X 0 X X X X 0 0 0 X 0 X X 0 X 0 0 0 0 0 X
generates a code of length 58 over Z2[X]/(X^2) who´s minimum homogenous weight is 50.
Homogenous weight enumerator: w(x)=1x^0+38x^50+42x^51+67x^52+70x^53+80x^54+82x^55+71x^56+62x^57+43x^58+62x^59+57x^60+82x^61+57x^62+70x^63+40x^64+42x^65+27x^66+11x^68+4x^70+7x^72+3x^74+1x^76+3x^78+1x^80+1x^82
The gray image is a linear code over GF(2) with n=116, k=10 and d=50.
This code was found by Heurico 1.16 in 0.178 seconds.