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
 0  X  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  X  0  X  0  X  X  X  X  X  0  0  X  X  0  X  0  X  X  X  X  X  0  0  X  X  X  X  0  0  X  X  X  X  0  0  X  0  X  0  X  X  X  X  X  X  0  0  0  0  0  0  0  X  X  0  X  X  0
 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  X  X  X  X  X  X  X  X  X  X  0  0  0  X  0  X  X  X  X  0  0  X  X  X  X  0  0  X  X  X  X  X  X  X  X  0  0  0  0  0  0  0  0  0  0  X  X  0  X  X  0  0
 0  0  0  X  0  0  0  0  0  0  0  X  X  X  X  X  X  X  X  X  X  X  0  0  0  0  X  X  X  X  0  0  0  X  0  X  X  0  X  0  X  X  0  0  X  X  0  X  X  0  0  0  X  0  0  0  X  0  X  X  X  X  0  0  0  0  0  0  X  X  X  0  X  X  X  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  X  X  0  X  0  X  X  X  X  X  X  X  0  X  0  X  X  X  X  0  X  0  X  X  X  X  0  X  X  0  0  X  X  0  0  0  0  X  X  0  0  0  0  X  X  0  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  0  0  0  0  X  X  X  X  X  X  X  0  0  0  X  0  X  0  X  0  X  X  0  X  0  X  X  X  0  X  0  0  X  X  0  X  X  X  X  X  0  0  X  X  0  0  0  0  X  X  X  X  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  0  X  X  0  X  0  0  X  0  X  X  X  0  0  0  X  0  X  X  X  X  X  0  X  X  0  X  0  0  X  0  X  0  0  0  X  0  0  0  X  0  X  X  0  0  0  0  0  0  X  X  0  0

generates a code of length 77 over Z2[X]/(X^2) who´s minimum homogenous weight is 72.

Homogenous weight enumerator: w(x)=1x^0+26x^72+12x^74+32x^75+24x^76+64x^77+28x^78+32x^79+13x^80+20x^82+3x^86+1x^150

The gray image is a linear code over GF(2) with n=154, k=8 and d=72.
This code was found by Heurico 1.16 in 0.0974 seconds.