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 1 X 0 X X 1 1 0 0 0 1 1 0 0 1 0 X 1 1 0 1 1 X X 1 X 0 X 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+1 0 1 1 0 1 X+1 X+1 X 1 1 1 0 1 0 X X 1 X+1 1 1 X 1 1 1 1 X+1 1 0 0 X 1 1 1 X 0 X
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 0 1 X 1 1 1 1 1 1 1 X+1 0 1 X X 0 X 1 X+1 X X+1 X+1 1 X 0 1 1 X 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 0 0 X+1 X+1 X 0 X+1 1 X+1 X+1 X+1 1 X+1 0 X X+1 0 0 X X+1 0 X+1 X+1 X+1 0 0 X 1 X+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 0 0 X+1 1 1 X+1 0 0 1 X 0 1 1 X 0 X+1 X 1 X+1 X X+1 X+1 1 X+1 0 0 1 X
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 X 0 0 X 0 0 X X 0 0 X X X X X X 0 X 0 X X 0 0 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 0 X X 0 X 0 X 0 0 0 X X X X X 0 X 0 X X X X 0 0 0 X 0 0 X 0 X X 0 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 0 0 0 0 0 X X X X X X X X X X X X X X 0 0 X X X X X 0 0 X X 0 X X X X 0 0 0 0 0 X
generates a code of length 64 over Z2[X]/(X^2) who´s minimum homogenous weight is 53.
Homogenous weight enumerator: w(x)=1x^0+96x^53+189x^54+178x^55+326x^56+362x^57+393x^58+460x^59+466x^60+476x^61+443x^62+524x^63+468x^64+488x^65+506x^66+442x^67+474x^68+434x^69+358x^70+332x^71+227x^72+164x^73+131x^74+98x^75+76x^76+26x^77+25x^78+14x^79+9x^80+2x^81+2x^82+1x^86+1x^88
The gray image is a linear code over GF(2) with n=128, k=13 and d=53.
This code was found by Heurico 1.16 in 70.8 seconds.