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

generates a code of length 79 over Z2[X]/(X^2) who´s minimum homogenous weight is 74.

Homogenous weight enumerator: w(x)=1x^0+15x^74+30x^76+32x^77+26x^78+64x^79+15x^80+32x^81+16x^82+18x^84+6x^86+1x^154

The gray image is a linear code over GF(2) with n=158, k=8 and d=74.
This code was found by Heurico 1.16 in 0.094 seconds.