The generator matrix

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

generates a code of length 80 over Z2[X]/(X^4) who´s minimum homogenous weight is 76.

Homogenous weight enumerator: w(x)=1x^0+36x^76+362x^77+345x^78+286x^79+221x^80+224x^81+189x^82+176x^83+80x^84+66x^85+12x^86+30x^87+6x^88+4x^89+4x^90+4x^91+1x^102+1x^114

The gray image is a linear code over GF(2) with n=640, k=11 and d=304.
This code was found by Heurico 1.16 in 2.06 seconds.