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 1 X X X X X X X X X X 1 1 0 X X 0 1 X 0 0 X 1 0 1 1 1 X X X
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 X 0 X 0 X X X X 0 X 0 X 0 0 0 X X 0 X X 0 X X X 0 X X X X 0 X X X 0 X X 0 X X X X X 0 0 X X 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 X 0 X 0 0 0 X X X 0 0 0 X 0 0 0 X 0 0 X X 0 0 X X 0 X 0 0 X 0 X X X X 0 X X X 0 X X X X 0 0 X 0 X 0 X
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 X X 0 X X 0 0 0 X 0 0 0 X 0 X X 0 0 X 0 0 X X 0 X 0 X 0 X 0 0 0 X 0 X X 0 X X X X X 0 X 0 0 X 0 X X X X
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 0 0 0 0 X X X X 0 0 0 X X 0 0 0 0 0 0 X X X X 0 X 0 0 0 X X X 0 X 0 0 0 X 0 0 X X 0 0 X 0 0 X X X 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 0 X X 0 0 0 0 0 0 X X 0 0 0 0 X 0 X X X 0 X X X X 0 0 0 0 X X 0 0 X X 0 0 X X X X X X 0 X 0 X 0 0 X X
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 0 0 X X 0 0 X X 0 0 X X 0 0 X X X X X X 0 0 0 0 0 X X 0 X X X 0 X X 0 0 X 0 X 0 0 0 X 0 0 X 0 X 0
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 X X X 0 X 0 X X X 0 0 X 0 X X 0 X 0 X X X 0 0 0 X 0 0 0 0 X 0 X 0 X X 0 X X X X 0 X X 0 X X X X 0 0 0 X
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 X 0 X X X 0 X X X 0 X X X 0 X X 0 X 0 X 0 X X X X 0 X X 0 X 0 0 0 X X X X X 0 X 0 X 0 0 0 0 0 0 0 0 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 0 0 X X 0 X X X X 0 0 X X X 0 X X 0 X X 0 X 0 X X X 0 X X X X 0 X X X X 0 0 X 0 X X X 0 X X X 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 X 0 0 0 X 0 0 0 0 0 X 0 X X 0 X X 0 X 0 X X X 0 X X 0 X X X 0 X X 0 X 0 X X X X 0 0 X X 0 X X 0 0 0 X
generates a code of length 78 over Z2[X]/(X^2) who´s minimum homogenous weight is 64.
Homogenous weight enumerator: w(x)=1x^0+165x^64+6x^66+302x^68+88x^70+467x^72+238x^74+636x^76+352x^78+643x^80+258x^82+396x^84+72x^86+264x^88+10x^90+124x^92+54x^96+14x^100+5x^104+1x^112
The gray image is a linear code over GF(2) with n=156, k=12 and d=64.
This code was found by Heurico 1.16 in 5.49 seconds.