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

generates a code of length 80 over Z2[X]/(X^3) who´s minimum homogenous weight is 77.

Homogenous weight enumerator: w(x)=1x^0+30x^77+123x^78+162x^79+68x^80+28x^81+29x^82+4x^83+6x^84+10x^85+18x^86+18x^87+4x^88+4x^89+5x^94+1x^96+1x^98

The gray image is a linear code over GF(2) with n=320, k=9 and d=154.
This code was found by Heurico 1.11 in 0.125 seconds.