The generator matrix

 1  0  1  1  1 X^2+X  1  1 X^3+X  1  1 X^3+X^2  1  1 X^3+X^2  1  1 X^3+X  1  1 X^2+X  1  1  0  1  1 X^3  1  1 X^3+X^2+X  1  1  1  1 X^2  X  1  1  1  1 X^3 X^3+X^2+X  1  1  1  1 X^2  X  X  X  0  X  X X^3+X^2  1  1  X  X  0  X  X  1  1 X^3+X^2 X^3+X^2 X^3+X^2  X  X X^2  1  1 X^3+X  X  X  X  1  X  1 X^2+X  1
 0  1 X+1 X^2+X X^2+1  1 X^3+X^2 X^3+X^2+X+1  1 X^3+X X^3+1  1  0 X+1  1 X^2+X X^2+1  1 X^3+X^2 X^3+X^2+X+1  1 X^3+X X^3+1  1 X^3 X^3+X+1  1 X^3+X^2+X X^3+X^2+1  1 X^2  X X^2+X+1  1  1  1 X^3 X^3+X^2+X X^3+X+1 X^3+X^2+1  1  1 X^2  X X^2+X+1  1  1  1  0 X^2+X  X X^3+X^2 X^3+X  X  0 X^3 X^3 X^2+X  X X^3+X^2 X^3+X X^3+X^2+X+1 X^3+X^2+X+1  X  1  1 X^2  X  X X^3+X X^3+1  1  0 X^3+X^2+X X^2 X^2+X  X X^2+1  1  0
 0  0 X^3 X^3  0 X^3 X^3  0  0  0 X^3 X^3 X^3  0  0  0 X^3 X^3  0 X^3  0 X^3  0 X^3 X^3 X^3 X^3  0  0  0  0 X^3  0 X^3  0 X^3  0 X^3  0 X^3  0 X^3 X^3  0 X^3  0 X^3  0 X^3 X^3 X^3 X^3 X^3 X^3  0 X^3  0  0  0  0  0  0 X^3  0  0 X^3 X^3 X^3 X^3  0  0 X^3  0  0  0 X^3  0 X^3  0  0

generates a code of length 80 over Z2[X]/(X^4) who´s minimum homogenous weight is 78.

Homogenous weight enumerator: w(x)=1x^0+60x^78+184x^79+89x^80+96x^81+18x^82+32x^83+22x^84+4x^85+2x^86+4x^89

The gray image is a linear code over GF(2) with n=640, k=9 and d=312.
This code was found by Heurico 1.16 in 0.344 seconds.