The generator matrix
1 0 0 0 0 1 1 1 0 1 1 X 1 0 1 0 0 1 X 1 1 X 0 X 1 1 X 1 1 X 0 1 1 X 0 1 X 1 X X 1 1 X 0 1 1 X 1 X 1 X X X 1 X 0 1
0 1 0 0 0 0 0 0 0 1 1 1 1 1 X+1 X 1 1 1 1 X 0 1 0 X 0 1 X 0 1 1 X+1 X 1 1 1 X 0 0 1 1 X+1 1 1 X X+1 1 1 1 0 1 X 1 1 1 X 0
0 0 1 0 0 0 1 1 1 1 X+1 0 0 X+1 X 0 X+1 1 X X+1 0 1 X 1 0 X+1 X+1 1 X 0 X+1 X 0 1 X 0 1 1 1 1 X+1 0 1 0 X+1 0 0 X X+1 X 0 X 1 0 X 0 0
0 0 0 1 0 1 1 0 1 X X+1 1 0 1 1 X X X X+1 1 1 X+1 X X 0 1 0 X 0 0 0 X X+1 0 0 X+1 1 0 1 X X 0 X+1 X X+1 1 0 X+1 1 X+1 X 1 X X 1 1 0
0 0 0 0 1 1 0 1 X+1 X X+1 X+1 1 X 0 1 1 0 X+1 1 X+1 1 X 0 0 X+1 1 X 1 X+1 X 0 X 0 X+1 X+1 0 X X 0 0 X+1 X X+1 0 X 1 1 X+1 X 1 1 X X 1 1 0
0 0 0 0 0 X 0 0 X 0 X X X X 0 X 0 X 0 0 0 0 X X X X X X X X 0 X 0 X X 0 X X 0 0 X X 0 0 X X 0 X X X X X X X X X 0
0 0 0 0 0 0 X 0 0 0 0 0 X 0 0 X X X X 0 0 X 0 0 X X 0 0 X X 0 X 0 0 0 X X 0 X X X 0 X X X X X X X 0 0 0 X X X X 0
0 0 0 0 0 0 0 X 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 X X X X X X X X X X X 0 X X X X 0 0 X X X X X 0 0 X 0 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+91x^46+140x^47+224x^48+256x^49+329x^50+406x^51+445x^52+420x^53+501x^54+574x^55+445x^56+532x^57+525x^58+548x^59+497x^60+468x^61+403x^62+376x^63+315x^64+204x^65+177x^66+118x^67+103x^68+40x^69+21x^70+14x^71+15x^72+1x^74+2x^76+1x^92
The gray image is a linear code over GF(2) with n=114, k=13 and d=46.
This code was found by Heurico 1.16 in 8.29 seconds.