The generator matrix

 1  0  0  0  0  0  1  1  1  X  0  0  0  0  1  1  1  X  X  0  1  1  1  1  0  1  1  1  0  0  0  X  1  X  1  1  1  1  1  1  0  0  1  0  X  0  X  1  X  0  1  X  0  1  X  0  1  0  1  X  1  1  1  1
 0  1  0  0  0  0  0  0  0  0  1  X  1  1  0  1  X  X  1  1  X  1  0  1  0 X+1  X  0  X  1  1  X X+1  1 X+1  1  1 X+1  1  0  X  1  X  X  0  X  0  0  1  1  1  0  X  0  1  0  X  X  1  0  X  1  X X+1
 0  0  1  0  0  0  0  0  0  0  X  1  1 X+1 X+1 X+1  1  1  0  X  0  0 X+1 X+1  1  1  X X+1  1  1  1  X  1  1 X+1  X X+1  X  0  1  1  X  0  1  1  1  X  0  1  0  1  1  1  1 X+1  1  0  1 X+1  0 X+1 X+1  1 X+1
 0  0  0  1  0  0  0  1  1  1 X+1 X+1  1  X  0 X+1  1  1  0  1 X+1  X  1  X  X  0  0  X  1  X  0  1  1 X+1  0 X+1  1  X  X  1  X  1  X  X  1  0  X X+1 X+1  X  X  X  1  1  1  X  0  0  1  1  X  1 X+1 X+1
 0  0  0  0  1  0  1  1  X X+1  1  1  1  0 X+1  0  X  X X+1  X X+1 X+1  1  X X+1 X+1  1  X  X  0  1  0  X  0  X X+1 X+1  X X+1 X+1 X+1  X  1  X  1  0  1 X+1  X  0  0 X+1  0  0  0  X  1 X+1  X  0  0  X  1 X+1
 0  0  0  0  0  1  1  X X+1  1  0  X  1 X+1  0 X+1  0  1 X+1 X+1  X  0 X+1  X X+1  1 X+1 X+1  1  1  X  0 X+1  0  X X+1  0 X+1  X  1 X+1 X+1  X  X  1  1 X+1  1  0 X+1 X+1  X  0  1  X  1  X  0 X+1 X+1  1  0  0  1
 0  0  0  0  0  0  X  0  X  0  0  0  0  0  X  X  X  0  0  0  X  X  X  X  0  0  0  0  X  X  X  X  0  X  0  X  0  X  0  0  X  X  0  0  X  X  X  0  0  X  0  0  0  X  0  X  X  X  0  X  X  X  0  0

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+100x^53+184x^54+232x^55+249x^56+336x^57+467x^58+446x^59+468x^60+450x^61+494x^62+484x^63+457x^64+498x^65+487x^66+498x^67+442x^68+426x^69+350x^70+278x^71+245x^72+198x^73+173x^74+104x^75+56x^76+40x^77+19x^78+6x^79+1x^82+2x^84+1x^94

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 73.5 seconds.