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

generates a code of length 76 over Z2[X]/(X^2) who´s minimum homogenous weight is 72.

Homogenous weight enumerator: w(x)=1x^0+16x^72+8x^73+10x^74+24x^75+12x^76+24x^77+12x^78+8x^79+3x^80+9x^82+1x^146

The gray image is a linear code over GF(2) with n=152, k=7 and d=72.
This code was found by Heurico 1.16 in 0.0779 seconds.