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  1  X  X  1  X  1  X  X  1  0  1  X  1  1  X  X  1  0  X  X  1  0  1  1  X  0  0  0  1  1  1
 0  X  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  X  X  X  X  X  X  X  X  X  X  X  X  X  X  X  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  X  X  X  X  X  X  X  X  X  X  X  X  X  X  X  0  X  X  X  X  0  X  0  X  X  0  0  X  X  X  X  X
 0  0  X  0  0  0  0  0  0  0  X  X  X  X  X  X  X  X  X  0  X  X  0  0  X  X  X  X  0  0  0  0  0  0  0  0  0  0  0  0  X  X  X  X  X  X  X  X  X  X  X  X  X  X  X  X  X  0  X  0  0  X  0  X  X  0  0  0  0  X  X  0  X  X  X  0  X  X  0  0
 0  0  0  X  0  0  0  X  X  X  X  X  0  X  X  0  0  0  0  0  0  0  0  0  X  X  X  X  X  X  X  X  0  0  0  0  X  X  X  X  X  X  X  X  0  0  0  0  0  0  0  0  0  0  0  0  X  X  X  X  0  X  X  0  X  0  X  X  X  X  0  0  X  0  X  X  0  X  X  0
 0  0  0  0  X  0  X  X  X  0  0  0  0  X  X  X  X  0  0  0  X  X  X  X  X  X  0  0  0  0  X  X  0  0  X  X  X  X  0  0  0  0  X  X  X  X  0  0  0  0  0  0  X  X  X  X  X  0  0  X  X  X  0  0  X  0  0  X  X  0  X  0  0  X  X  X  X  X  X  X
 0  0  0  0  0  X  X  0  X  X  0  X  X  X  0  0  X  0  X  X  X  0  0  X  0  X  X  0  0  X  X  0  0  X  X  0  0  X  X  0  0  X  X  0  0  X  X  0  0  X  0  X  X  X  0  0  0  0  0  0  0  0  X  X  X  0  0  X  X  0  X  X  X  0  X  0  0  X  X  0

generates a code of length 80 over Z2[X]/(X^2) who´s minimum homogenous weight is 77.

Homogenous weight enumerator: w(x)=1x^0+40x^77+25x^78+25x^80+24x^85+6x^86+6x^88+1x^126

The gray image is a linear code over GF(2) with n=160, k=7 and d=77.
This code was found by Heurico 1.16 in 9.55 seconds.