The generator matrix
1 0 0 1 1 1 0 1 1 1 1 1 0 X 0 1 0 1 1 0 X 1 1 X 0 1 1 1 0 0 0 1 1 1 X 1 X 1 1 0 1 1 1 X X 1 1 X X 1 0 1 1 1 0 X 1
0 1 0 1 0 1 1 0 0 1 X+1 X 1 1 0 X 0 X+1 X+1 1 1 0 1 0 1 1 1 1 1 0 1 X+1 X 1 1 X X X X 1 X+1 1 X+1 1 1 1 1 X 1 X+1 X X X+1 X 1 X 0
0 0 1 1 1 0 1 0 1 X+1 X 1 X 1 1 0 1 X+1 0 0 1 X+1 X+1 1 0 1 1 X X+1 1 X 0 1 X X+1 0 1 1 X 1 X+1 X+1 0 X+1 1 X X+1 1 1 0 1 0 0 0 0 1 0
0 0 0 X 0 0 0 0 0 X 0 0 0 0 0 0 0 X 0 0 0 0 X 0 X X X X 0 X 0 X X 0 X X 0 0 X X 0 X X X X 0 0 X 0 X 0 X X X 0 0 0
0 0 0 0 X 0 0 0 0 0 0 0 X X X X 0 X 0 X 0 X X 0 0 X X 0 X 0 X X 0 X 0 X 0 0 0 X 0 X 0 X X 0 0 0 0 X X 0 0 X X 0 0
0 0 0 0 0 X 0 0 0 0 X 0 0 0 0 0 0 0 X X 0 X X X 0 0 X X X X 0 X 0 X 0 0 X X X X X 0 X 0 0 0 X 0 0 X X X 0 X X 0 0
0 0 0 0 0 0 X 0 0 0 0 0 0 X 0 0 X X X X X X 0 0 X 0 X X 0 X 0 0 X X X 0 X 0 0 0 X 0 X X X 0 0 0 X X X 0 X X X X 0
0 0 0 0 0 0 0 X 0 X X X 0 0 X 0 X X X 0 X X 0 X 0 0 0 0 0 X 0 X 0 0 0 X X X 0 X 0 X 0 X 0 X X X 0 X 0 X X X 0 0 0
0 0 0 0 0 0 0 0 X 0 0 X X X X X 0 X 0 X X 0 X 0 X 0 0 X 0 X 0 X X 0 0 0 0 X 0 X X 0 0 X 0 0 0 X X 0 X X 0 X 0 X 0
generates a code of length 57 over Z2[X]/(X^2) who´s minimum homogenous weight is 46.
Homogenous weight enumerator: w(x)=1x^0+25x^46+54x^47+124x^48+124x^49+152x^50+226x^51+225x^52+224x^53+244x^54+262x^55+282x^56+290x^57+277x^58+260x^59+236x^60+256x^61+198x^62+146x^63+103x^64+112x^65+98x^66+74x^67+41x^68+16x^69+20x^70+2x^71+10x^72+2x^73+9x^74+2x^76+1x^78
The gray image is a linear code over GF(2) with n=114, k=12 and d=46.
This code was found by Heurico 1.16 in 2.16 seconds.