The generator matrix

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

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+72x^54+126x^55+135x^56+220x^57+230x^58+232x^59+244x^60+220x^61+250x^62+242x^63+243x^64+278x^65+247x^66+210x^67+229x^68+202x^69+177x^70+136x^71+93x^72+94x^73+57x^74+70x^75+42x^76+10x^77+19x^78+8x^79+4x^80+2x^82+1x^84+2x^86

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 2.16 seconds.