The generator matrix
1 0 0 0 1 1 1 0 1 1 1 1 X X X X 0 1 0 1 X 1 1 1 1 X 1 1 0 1 X X 0 X 0 1 0 0 1 1 1 1 1 X 1 X 1 1 1 1 X X 0
0 1 0 0 0 1 1 1 0 0 1 X+1 1 0 1 1 X X 0 X+1 1 X 1 1 X+1 1 X 0 0 X X 1 X 1 1 X+1 1 0 X+1 X+1 0 1 0 X 1 0 0 X 0 X+1 X 1 1
0 0 1 0 1 1 0 1 0 1 1 0 0 1 1 X 1 0 X 0 1 X+1 1 X+1 0 X X+1 X 1 0 1 0 1 X+1 0 X+1 1 0 1 X 1 1 X 1 X+1 1 X+1 1 1 1 X 0 1
0 0 0 1 1 0 1 1 1 0 1 0 1 1 0 X X 1 1 X X+1 1 X X+1 1 1 X 0 X+1 0 0 1 1 X 0 X X 1 1 0 X 1 X 1 X+1 0 X+1 1 1 X 1 X X
0 0 0 0 X 0 0 0 0 0 0 0 0 X 0 0 0 0 0 0 0 X X X X X 0 X 0 X 0 X 0 0 0 X 0 X X X 0 0 X 0 X X X 0 X 0 X X 0
0 0 0 0 0 X 0 0 0 0 0 0 0 X X 0 X X X X 0 0 0 0 X 0 X 0 X 0 0 X X X 0 X 0 X X X 0 0 X X X 0 0 X 0 0 X X X
0 0 0 0 0 0 X 0 0 0 0 X 0 0 X X 0 0 X X 0 X X 0 X 0 0 X 0 X 0 0 0 X X X 0 0 X 0 X X 0 X X X X 0 X 0 0 0 0
0 0 0 0 0 0 0 X 0 0 0 X 0 0 X X 0 0 X X X X 0 X 0 0 0 X X 0 0 X X 0 0 X X X X X X X X X X X 0 X 0 X X 0 0
0 0 0 0 0 0 0 0 X 0 0 0 X 0 0 0 0 X 0 0 0 0 0 0 X X X X X X X X X 0 X 0 0 0 0 X X 0 0 X X 0 X X 0 0 X X X
0 0 0 0 0 0 0 0 0 X 0 0 X 0 X X 0 0 X X X 0 X 0 X X 0 0 0 0 0 X 0 X 0 0 X X X 0 0 0 X 0 X X X X X X 0 0 X
0 0 0 0 0 0 0 0 0 0 X X X X 0 0 X X X X X X X X X 0 0 0 X X 0 X 0 0 X X 0 0 0 0 X X X 0 X X 0 X 0 X 0 X X
generates a code of length 53 over Z2[X]/(X^2) who´s minimum homogenous weight is 39.
Homogenous weight enumerator: w(x)=1x^0+38x^39+117x^40+170x^41+354x^42+464x^43+615x^44+786x^45+1089x^46+1214x^47+1445x^48+1818x^49+2026x^50+2408x^51+2520x^52+2436x^53+2402x^54+2438x^55+2242x^56+1998x^57+1597x^58+1280x^59+967x^60+820x^61+573x^62+306x^63+236x^64+142x^65+132x^66+40x^67+42x^68+20x^69+16x^70+4x^71+7x^72+3x^74+2x^77
The gray image is a linear code over GF(2) with n=106, k=15 and d=39.
This code was found by Heurico 1.16 in 96 seconds.