The generator matrix

 1  0  1  1  1 X^2+X  1  1 X^2  1  1 X^2  X  X  1  1  1  1  0  1  1 X^2+X  1  1  1  1  1  1  0  1  1  X X^2+X  0  1 X^2+X  1  1  1  1  1  1  1  0  1  1 X^2 X^2+X  1  X  1  1  X  1  0 X^2  X  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  X  1  0  1  1  1
 0  1  1 X^2+X X+1  1 X^2+1 X^2  1  X X^2+X+1  1  1  1  0  1 X^2+X X^2  1 X^2+X+1  X  1  1 X^2+X+1 X^2+X+1  1 X+1  0  1 X^2+1  X  1  1  1  0  1 X^2+X X^2+X+1  1 X^2+X+1  0  1 X^2+X  1 X^2 X^2+X  1  1 X+1 X^2+X X+1  0 X^2  X  1  X  1 X+1 X+1 X+1 X^2+1 X^2+1  1 X^2+1 X^2+1 X^2+1 X^2+1 X^2+X+1 X+1 X^2+X+1 X^2+X+1  X  1  X  1 X^2  0 X^2 X^2+X X^2
 0  0  X  0 X^2  0 X^2  X  X  X  X X^2+X  0  X  0 X^2+X X^2+X X^2+X  0 X^2  0 X^2+X X^2 X^2+X  X  X  0 X^2+X X^2+X  0 X^2+X X^2+X X^2  X  X  X  X X^2+X X^2+X  0 X^2  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2+X  0 X^2+X X^2 X^2  0 X^2 X^2  0  X  X  0  0 X^2+X X^2  0  X X^2+X  X  0 X^2 X^2  0  X  X X^2+X X^2+X  0  X  X  X X^2
 0  0  0 X^2 X^2 X^2  0 X^2 X^2  0 X^2  0  0  0 X^2  0 X^2  0 X^2 X^2  0 X^2  0 X^2  0 X^2  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2  0  0  0 X^2  0  0 X^2 X^2  0 X^2  0 X^2  0  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2  0  0 X^2 X^2 X^2 X^2  0  0  0 X^2 X^2 X^2 X^2  0  0 X^2  0  0  0  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+68x^77+107x^78+76x^79+82x^80+60x^81+18x^82+36x^83+41x^84+14x^85+3x^86+1x^88+1x^92+2x^101+1x^104+1x^112

The gray image is a linear code over GF(2) with n=320, k=9 and d=154.
This code was found by Heurico 1.16 in 0.36 seconds.