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 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X X X X X X X X X X X 0 X 1 0 X 1 X X 0 1 X 1 X 0 1 1 1 1
0 X 0 0 0 0 0 0 0 0 0 0 0 0 X 0 0 0 0 0 0 0 0 0 X X X X X X X 0 X X X X 0 X 0 0 0 X X X 0 X X X 0 X 0 X 0 X X 0 0 0 X X 0 0 0 0 X 0 0 X 0 X X X X 0 0 0 0
0 0 X 0 0 0 0 0 0 0 0 0 0 0 X 0 0 0 0 X X X X X X X 0 0 0 X 0 0 0 X X X 0 0 0 X X X 0 X X 0 0 X X X 0 0 X 0 X 0 X 0 0 X 0 X X 0 0 X X 0 0 X X X X 0 0 0 0
0 0 0 X 0 0 0 0 0 0 0 0 0 X 0 0 0 X X X X X X 0 0 0 0 X 0 X X X 0 X 0 0 X X 0 0 0 X X X 0 X 0 X X X X X 0 0 0 0 0 0 0 X 0 0 0 X X X 0 0 0 0 X X X X 0 X 0
0 0 0 0 X 0 0 0 0 0 0 0 0 X 0 X X X X X X 0 X X 0 X X X 0 0 0 X X X X X 0 X X 0 0 0 X 0 0 0 0 X 0 0 0 0 0 X 0 X X X X X X 0 X 0 0 0 0 X X X 0 0 0 0 0 0 0
0 0 0 0 0 X 0 0 0 0 0 0 X 0 0 X X 0 X X 0 X 0 X 0 X X X X 0 0 X X 0 0 0 X 0 X 0 0 0 0 X X 0 X X X X 0 0 X 0 0 0 X X 0 X 0 X 0 X X X 0 0 0 X X X X 0 0 X 0
0 0 0 0 0 0 X 0 0 0 0 0 X 0 0 0 X X X X 0 X X 0 X 0 X 0 0 X 0 0 X X X 0 0 0 0 X 0 0 0 X X X X 0 X 0 0 X 0 0 0 X 0 X X X 0 X X X X 0 0 X 0 X X 0 0 X X 0 X
0 0 0 0 0 0 0 X 0 0 0 X 0 0 0 0 X X 0 X 0 0 0 X X X 0 0 X 0 X X X X 0 0 0 X X X X X 0 0 0 0 X X X X 0 X X X X 0 0 X X X 0 X X 0 0 X 0 X 0 X 0 X 0 X 0 X 0
0 0 0 0 0 0 0 0 X 0 0 X 0 0 0 X 0 0 X 0 X 0 0 X 0 0 0 0 X X X 0 0 X X 0 X X X X 0 0 0 X X X X 0 X X X X 0 X X 0 0 0 0 X X 0 0 0 X X X X 0 0 0 0 X 0 X 0 0
0 0 0 0 0 0 0 0 0 X 0 X X X X X 0 0 0 X 0 0 X X 0 0 X 0 X X 0 0 X X 0 X X 0 0 0 0 X 0 0 0 X 0 X 0 X X 0 X 0 X X 0 X 0 X 0 0 X 0 0 X 0 X X 0 0 0 X X 0 0 X
0 0 0 0 0 0 0 0 0 0 X X X X X 0 0 X X X X X 0 X 0 X 0 0 0 0 0 X 0 X 0 0 X 0 X X 0 0 0 X 0 0 X 0 0 0 0 X X X 0 X X X X 0 X X X 0 0 0 X 0 0 X 0 X X X X 0 0
generates a code of length 77 over Z2[X]/(X^2) who´s minimum homogenous weight is 62.
Homogenous weight enumerator: w(x)=1x^0+44x^62+97x^64+155x^66+212x^68+295x^70+391x^72+394x^74+470x^76+511x^78+448x^80+356x^82+220x^84+165x^86+127x^88+86x^90+54x^92+41x^94+21x^96+1x^98+4x^100+2x^104+1x^112
The gray image is a linear code over GF(2) with n=154, k=12 and d=62.
This code was found by Heurico 1.16 in 5.19 seconds.