The generator matrix
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X 1 X 1 1 1 1 1 X 1 1 X 1 X 1 X 1 1 1 1 1 X 1 1 X 1 1 X 1 0 1 1 1
0 X 0 0 0 0 0 0 0 0 0 X 0 0 X X 0 0 0 0 X X X X 0 X X 0 X X 0 X X X 0 X X 0 X 0 0 0 0 X X 0 X X X 0 X 0 0 0 0 X 0 X X X X X X 0
0 0 X 0 0 0 0 0 0 0 0 X X X X X 0 0 0 X X 0 0 0 0 0 0 X X 0 X 0 X X 0 X X X X X X 0 0 0 0 X X X 0 0 0 0 0 X X X X 0 X 0 X 0 0 0
0 0 0 X 0 0 0 0 0 0 X 0 X X 0 X X 0 X 0 X X X X 0 X 0 X 0 0 0 X X X X 0 0 X 0 0 0 X X X X X X X X 0 X X X 0 0 X 0 0 X 0 X 0 0 0
0 0 0 0 X 0 0 0 0 0 X 0 0 X X X X X 0 X 0 0 0 0 0 X X 0 X X 0 X X 0 0 X 0 0 X X X 0 0 0 0 0 0 X X X 0 0 X X X X 0 X 0 X 0 X X X
0 0 0 0 0 X 0 0 0 X 0 0 0 X X 0 X 0 X X X 0 0 X 0 X X X X X X 0 X X X 0 0 0 X 0 0 X 0 X 0 X 0 0 X X X 0 0 0 X X 0 X 0 0 0 0 X 0
0 0 0 0 0 0 X 0 0 X 0 0 X 0 0 X X X 0 X X 0 X X 0 0 X 0 0 0 X X X 0 X 0 X 0 X X 0 0 X X X 0 0 0 X X 0 0 0 0 X 0 X 0 X X X X X X
0 0 0 0 0 0 0 X 0 X X X X 0 0 0 0 0 X X X X X 0 X X 0 X X X 0 0 0 0 0 X X X 0 X 0 0 0 0 X 0 X 0 0 0 X X 0 0 0 0 X 0 X X 0 X X 0
0 0 0 0 0 0 0 0 X X X X 0 0 X X X 0 0 0 X 0 0 0 X 0 X 0 0 X X 0 X 0 0 X 0 X 0 0 0 0 X X X X 0 X X 0 X X X X 0 0 X 0 X 0 0 X 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+36x^54+71x^56+90x^58+112x^60+142x^62+181x^64+136x^66+75x^68+64x^70+43x^72+26x^74+17x^76+14x^78+8x^80+4x^82+3x^84+1x^108
The gray image is a linear code over GF(2) with n=128, k=10 and d=54.
This code was found by Heurico 1.16 in 0.269 seconds.