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.