The generator matrix

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

generates a code of length 64 over Z2[X]/(X^2) who´s minimum homogenous weight is 54.

Homogenous weight enumerator: w(x)=1x^0+49x^54+102x^55+175x^56+210x^57+203x^58+266x^59+280x^60+260x^61+252x^62+238x^63+237x^64+228x^65+237x^66+214x^67+187x^68+220x^69+170x^70+136x^71+106x^72+82x^73+90x^74+64x^75+33x^76+24x^77+21x^78+4x^79+5x^80+2x^82

The gray image is a linear code over GF(2) with n=128, k=12 and d=54.
This code was found by Heurico 1.16 in 2.22 seconds.