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

generates a code of length 77 over Z2[X]/(X^2) who´s minimum homogenous weight is 73.

Homogenous weight enumerator: w(x)=1x^0+20x^73+15x^74+15x^76+32x^77+14x^78+14x^80+4x^81+1x^82+1x^84+8x^85+1x^86+1x^88+1x^126

The gray image is a linear code over GF(2) with n=154, k=7 and d=73.
This code was found by Heurico 1.16 in 1.4 seconds.