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

generates a code of length 78 over Z2[X]/(X^2) who´s minimum homogenous weight is 74.

Homogenous weight enumerator: w(x)=1x^0+10x^74+8x^75+18x^76+24x^77+14x^78+24x^79+7x^80+8x^81+6x^82+6x^84+1x^86+1x^150

The gray image is a linear code over GF(2) with n=156, k=7 and d=74.
This code was found by Heurico 1.16 in 0.111 seconds.