The generator matrix

1 0 0 0 0 0 1 1 1 X 1 1 0 0 1 1 1 1 X 1 X 1 X 1 1 X 0 X X X 1 1 0 1 1 1 1 X X X 1 0 0 0 0 X 1 1 1 1 1 1 0 0 1 0 1 1 0 X 1 1 0 1
0 1 0 0 0 0 0 0 0 0 0 0 X 1 1 X+1 1 X+1 1 X+1 X X 1 X+1 1 1 1 X 1 1 0 X 1 1 X X+1 X+1 0 1 1 X 1 1 1 1 X 1 1 1 0 1 0 X 1 1 1 X X+1 X 1 1 1 0 0
0 0 1 0 0 0 0 0 X X 1 1 1 X 0 0 X+1 X+1 X+1 1 1 1 1 X X+1 X 1 1 1 X 1 0 0 X+1 0 X X+1 0 0 1 0 X+1 X 0 0 X 1 X+1 0 0 X 0 1 X+1 X 1 X 1 1 X 0 X+1 0 0
0 0 0 1 0 0 1 X 1 1 0 X+1 1 1 X X+1 X+1 0 0 1 1 X X X 0 1 X+1 0 1 X 1 X+1 X 0 X X+1 X+1 1 X+1 X+1 0 X+1 0 1 X+1 1 1 0 X 1 X+1 1 0 0 0 X+1 X X 0 X X X X 0
0 0 0 0 1 0 1 X+1 0 1 X X+1 1 1 0 1 0 X 1 1 0 X+1 X 1 X+1 X X+1 X+1 X 1 0 X+1 1 1 1 0 0 X+1 0 1 X X 1 1 0 0 X+1 X X X+1 1 1 X 0 0 0 1 X X+1 0 X+1 1 0 X
0 0 0 0 0 1 X 1 1 X+1 1 X+1 0 X X+1 1 1 X 0 0 1 X 1 X X+1 1 1 1 0 1 X+1 X+1 X X 0 X+1 X X 0 X 1 0 0 1 1 X+1 X+1 0 0 0 1 0 1 1 0 X+1 1 1 X+1 X+1 X+1 0 1 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+78x^54+110x^55+130x^56+192x^57+261x^58+270x^59+235x^60+268x^61+225x^62+244x^63+247x^64+212x^65+203x^66+246x^67+243x^68+180x^69+173x^70+144x^71+131x^72+92x^73+68x^74+68x^75+30x^76+16x^77+16x^78+6x^79+7x^80

The gray image is a linear code over GF(2) with n=128, k=12 and d=54.
This code was found by Heurico 1.10 in 0.812 seconds.