The generator matrix

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

generates a code of length 79 over Z2[X]/(X^2) who�s minimum homogenous weight is 76.

Homogenous weight enumerator: w(x)=1x^0+70x^76+82x^78+49x^80+28x^82+7x^84+6x^86+7x^88+4x^90+1x^92+1x^120

The gray image is a linear code over GF(2) with n=158, k=8 and d=76.
This code was found by Heurico 1.16 in 0.0958 seconds.