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  X  X  0  X X^2  0  X  X  0  X  X  X  0  X X^2 X^2  0  0  0  0  X  X X^2  X  X X^2  X  X  X  X  X X^2  1  1  1  1  X X^2  1  1  X  X  1  X  0  1  1
 0  X  0  X  0  0 X^2+X X^2+X  0  0  X  X  0  0 X^2+X X^2+X X^2 X^2  X X^2+X X^2 X^2 X^2+X  X X^2 X^2  X X^2+X X^2 X^2 X^2+X  X X^2  X  X X^2+X  X  0  0  X  X  X X^2+X X^2  0  0  X X^2  X  X X^2  X X^2+X  X  X X^2+X X^2  X  0  0 X^2 X^2  0  X  0  0 X^2 X^2 X^2  X  X X^2+X  0 X^2  X  0  X  0  0
 0  0  X  X  0 X^2+X X^2+X  0 X^2 X^2+X X^2+X X^2 X^2  X  X X^2 X^2  X  X  0 X^2  X X^2+X X^2  0 X^2+X X^2+X X^2  0 X^2+X  X  0  X  X X^2  0  X  X X^2+X X^2 X^2+X X^2+X  0  X  X X^2+X  X  X  0  0  X X^2 X^2  X X^2+X  X X^2+X X^2  0 X^2 X^2  0  X  0  0 X^2 X^2  0 X^2+X X^2  X X^2+X X^2  0  X X^2+X  0  0 X^2
 0  0  0 X^2 X^2 X^2  0 X^2 X^2  0 X^2  0  0 X^2  0 X^2  0  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2  0  0  0  0 X^2 X^2  0  0  0 X^2 X^2 X^2  0 X^2 X^2  0  0 X^2  0 X^2  0  0  0 X^2 X^2 X^2  0 X^2  0 X^2 X^2  0 X^2 X^2 X^2 X^2 X^2  0  0  0  0  0  0 X^2  0  0  0  0 X^2  0 X^2 X^2 X^2

generates a code of length 79 over Z2[X]/(X^3) who´s minimum homogenous weight is 77.

Homogenous weight enumerator: w(x)=1x^0+130x^77+24x^78+16x^79+23x^80+8x^81+7x^82+8x^84+36x^85+2x^93+1x^98

The gray image is a linear code over GF(2) with n=316, k=8 and d=154.
This code was found by Heurico 1.16 in 1.78 seconds.