The generator matrix
1 0 1 1 1 0 1 1 0 1 1 X 1 1 0 1 1 0 1 1 0 1 X 1 1 1 0 1 1 0 1 1 0 0 1 1 0 X 1 0 1 1 1 X 1 1 1 1 1 0 1 1 X 1 0 0 X 1
0 1 1 0 1 1 0 1 1 X X+1 1 0 X+1 1 X+1 0 1 0 X+1 1 X+1 1 0 X+1 1 1 X X+1 1 0 1 1 1 X+1 X+1 1 1 X+1 1 0 1 0 1 X X+1 X X X+1 1 0 X 1 1 0 1 0 0
0 0 X 0 0 0 0 0 0 0 X 0 0 0 0 0 X X X X X X X X 0 X X 0 X X X X X X X 0 X 0 X 0 X 0 0 X X X 0 X X X X X 0 X X X X 0
0 0 0 X 0 0 0 0 0 X 0 0 0 0 0 0 0 0 0 0 X 0 X X X X X X X 0 X 0 X X 0 0 X X X X X 0 X 0 0 X 0 0 X 0 0 0 X 0 0 X X 0
0 0 0 0 X 0 0 0 0 0 X 0 0 X X X X 0 X 0 0 0 X X 0 X X 0 X 0 0 X X 0 0 0 0 X 0 X 0 0 X X X 0 X X 0 X 0 X 0 0 X 0 0 0
0 0 0 0 0 X 0 0 0 0 0 X 0 X X 0 X X X X X 0 0 X X X X 0 0 0 0 X X X 0 0 0 0 X X 0 X 0 0 0 X 0 X 0 0 X 0 0 X 0 0 X 0
0 0 0 0 0 0 X 0 0 X 0 0 X X 0 X X 0 X X X X X X X 0 0 0 X X 0 0 0 0 0 0 X 0 X 0 0 0 X 0 X 0 X X 0 0 X 0 X 0 X X X 0
0 0 0 0 0 0 0 X 0 0 X 0 X 0 0 X X 0 0 X 0 0 0 X X X X X 0 X 0 0 0 0 X X X 0 X X 0 X X X X X 0 0 X X 0 X 0 0 0 X 0 0
0 0 0 0 0 0 0 0 X 0 0 X 0 X 0 X X X 0 0 0 X X 0 X X 0 X 0 X 0 0 X 0 0 X X X X 0 X 0 0 0 X X 0 X 0 X 0 0 X 0 0 0 X 0
generates a code of length 58 over Z2[X]/(X^2) who´s minimum homogenous weight is 48.
Homogenous weight enumerator: w(x)=1x^0+47x^48+34x^49+69x^50+74x^51+134x^52+114x^53+104x^54+148x^55+115x^56+136x^57+135x^58+152x^59+115x^60+152x^61+111x^62+108x^63+60x^64+70x^65+43x^66+30x^67+28x^68+6x^69+30x^70+9x^72+17x^74+3x^76+3x^78
The gray image is a linear code over GF(2) with n=116, k=11 and d=48.
This code was found by Heurico 1.16 in 0.62 seconds.