The generator matrix
1 0 0 0 0 1 1 1 0 1 1 X 1 0 1 0 0 1 0 1 X 1 1 1 0 1 X 1 X 0 1 1 1 1 X 1 X X 1 1 X 1 1 0 0 1 0 X 1 0 1
0 1 0 0 0 0 0 0 0 1 1 1 1 1 X+1 X 1 0 1 X 0 X 0 X 1 X+1 0 0 1 1 X 1 X 0 1 X+1 1 0 X+1 X 1 X+1 0 1 X X+1 1 1 X+1 1 0
0 0 1 0 0 0 1 1 1 1 X+1 0 0 X+1 X 0 X+1 0 X X+1 1 X X+1 0 1 X 0 0 0 X X+1 0 1 1 1 0 X X 1 1 X+1 X+1 X X+1 X 0 X+1 1 X 1 0
0 0 0 1 0 1 1 0 1 X X+1 1 0 1 1 X X X 0 X+1 X X+1 X+1 X 1 0 1 1 X 1 X X+1 1 1 0 1 0 1 0 1 1 X+1 1 0 0 1 1 X+1 X+1 X 0
0 0 0 0 1 1 0 1 X+1 X X+1 X+1 1 X 0 1 1 0 X X X X+1 X 1 X+1 X 1 0 1 0 0 1 X+1 1 X 0 X X 1 X+1 X+1 0 0 1 1 X+1 0 0 X 1 0
0 0 0 0 0 X 0 0 X 0 X X X X 0 X 0 X 0 X 0 0 0 X X X X X X 0 0 0 0 0 X 0 X 0 0 X 0 X X 0 0 X 0 X X X 0
0 0 0 0 0 0 X 0 0 0 0 0 X 0 0 X X X X X X X 0 0 X X 0 X X X X X 0 X 0 0 0 0 0 0 0 X 0 0 X 0 0 0 X 0 0
0 0 0 0 0 0 0 X 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 0 X 0 0 X X X X 0 X 0 X 0
generates a code of length 51 over Z2[X]/(X^2) who´s minimum homogenous weight is 40.
Homogenous weight enumerator: w(x)=1x^0+75x^40+84x^41+195x^42+260x^43+334x^44+376x^45+415x^46+450x^47+470x^48+614x^49+555x^50+560x^51+554x^52+568x^53+527x^54+516x^55+421x^56+320x^57+263x^58+236x^59+168x^60+80x^61+80x^62+26x^63+25x^64+6x^65+11x^66+1x^70+1x^78
The gray image is a linear code over GF(2) with n=102, k=13 and d=40.
This code was found by Heurico 1.16 in 6.72 seconds.