The generator matrix

 1  0  1  1  1  0  1  1  0  1  1  0  1  1  X  1  1  X  1  1  X  1  1  X  1  1  0  1  1  0  1  1  0  1  1  0  1  1  1  1  1  1  1  1  X  X  X  X  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
 0  1  1  0  1  1 X+1  0  1  0 X+1  1  X X+1  1  X  1  1  X X+1  1  X  1  1  0 X+1  1  0 X+1  1  0 X+1  1  0 X+1  1  X  1  X  1  X  X  1  1  1  1  1  1  0  0  0  0  0  0  0  0  X  X  X  X  X  X  X  X X+1 X+1 X+1  1 X+1 X+1 X+1  1 X+1  1  1  1 X+1  1
 0  0  X  0  0  0  0  X  X  X  X  X  X  0  X  X  0  X  0  X  0  0  X  0  0  0  0  X  X  X  0  0  X  X  X  0  X  X  X  X  0  0  0  0  X  X  0  0  0  0  0  0  X  X  X  X  X  X  X  X  0  0  0  0  0  0  0  0  X  X  X  X  0  X  X  0  X  X
 0  0  0  X  0  X  X  X  X  0  X  0  0  0  0  X  X  X  X  0  X  0  X  0  0  0  X  X  X  0  X  X  X  0  0  0  0  0  X  X  X  0  X  0  0  X  X  0  0  0  X  X  X  X  0  0  0  0  X  X  X  X  0  0  0  0  X  X  X  X  0  0  X  0  X  0  0  0
 0  0  0  0  X  0  X  X  X  X  0  X  X  X  X  X  X  X  0  0  0  0  0  0  X  0  X  0  X  0  X  0  0  0  X  X  0  X  0  X  X  X  0  0  0  0  X  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  X  X  0  0  0

generates a code of length 78 over Z2[X]/(X^2) who´s minimum homogenous weight is 76.

Homogenous weight enumerator: w(x)=1x^0+30x^76+64x^78+30x^80+1x^92+1x^96+1x^124

The gray image is a linear code over GF(2) with n=156, k=7 and d=76.
This code was found by Heurico 1.16 in 0.114 seconds.