The generator matrix

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

generates a code of length 80 over Z2[X]/(X^3) who´s minimum homogenous weight is 78.

Homogenous weight enumerator: w(x)=1x^0+26x^78+144x^79+27x^80+8x^81+2x^82+20x^83+2x^84+8x^85+2x^86+8x^87+2x^90+4x^91+2x^92

The gray image is a linear code over GF(2) with n=320, k=8 and d=156.
This code was found by Heurico 1.16 in 0.257 seconds.