The generator matrix

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

generates a code of length 79 over Z2[X]/(X^3) who´s minimum homogenous weight is 76.

Homogenous weight enumerator: w(x)=1x^0+64x^76+96x^77+122x^78+56x^79+65x^80+8x^81+40x^82+20x^83+9x^84+4x^85+14x^86+4x^87+2x^88+4x^89+2x^92+1x^100

The gray image is a linear code over GF(2) with n=316, k=9 and d=152.
This code was found by Heurico 1.16 in 0.174 seconds.