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 1 1 1 X 1 1 0 0 1 0 1 1 1 X 1 0 1 X 1 1 0 1 X X 1 X 1 1 1 X 0 1 0
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+1 0 1 1 0 1 X+1 X+1 1 X X 1 0 X+1 0 1 X 1 1 1 X+1 X X 1 1 0 X+1 1 X X+1 1 1 0 X+1 1
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 0 1 X 1 X+1 X+1 0 X 1 X 0 X 1 0 0 0 0 X+1 X X 1 X+1 1 X+1 X 1 1 1 X 1 X+1 X+1 1 X+1 X+1
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 0 X X 0 X X+1 1 1 1 1 0 X+1 1 X X 0 X X+1 0 X+1 0 0 0 0 1 0 1 0 0 1 1 1 X+1 0 1
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 1 X+1 1 X 1 0 X+1 X+1 1 X+1 1 0 X+1 X X+1 X+1 X 0 0 0 X+1 X 0 X+1 X 1 0 0 X+1 X X+1 0 X+1 X+1 1
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 0 X 0 0 0 0 0 X X 0 X 0 0 0 X 0 0 X 0 X 0 0 X X X 0 0 X 0 0 X
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 0 X X 0 X 0 0 X X 0 0 0 X X X X 0 0 X X X X X X X X 0 0 X 0 0 X X
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 0 X X X X X X X X X X X X X 0 X X X 0 X 0 0 X 0 X X 0 X 0 X X X X X X
generates a code of length 62 over Z2[X]/(X^2) who´s minimum homogenous weight is 51.
Homogenous weight enumerator: w(x)=1x^0+82x^51+170x^52+226x^53+288x^54+340x^55+395x^56+418x^57+480x^58+454x^59+473x^60+568x^61+544x^62+540x^63+476x^64+444x^65+427x^66+402x^67+399x^68+282x^69+238x^70+192x^71+107x^72+98x^73+68x^74+38x^75+21x^76+12x^77+2x^78+5x^80+1x^82+1x^84
The gray image is a linear code over GF(2) with n=124, k=13 and d=51.
This code was found by Heurico 1.16 in 67.4 seconds.