The generator matrix

 1  0  1  1  1 X^3+X^2+X  1  1 X^3+X^2  1  1  X  1  1 X^3  1 X^2+X  1  1 X^2  1  1  1 X^3+X  1  1  1  1  1 X^3  1 X^2+X  1  1 X^2  1  1 X^3+X  1  X  1  1  1  1  1 X^3 X^2+X  1 X^2 X^3+X  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  1  1  1  0 X^2  1  1 X^3+X^2+X X^3+X  1  1  1  X  X
 0  1 X+1 X^3+X^2+X X^2+1  1 X^3 X^2+X+1  1 X^3+X^2 X^3+1  1  X X+1  1 X^3+X^2+1  1 X^2+X  1  1 X^2 X^3+X X^3+X^2+X+1  1  0 X^3+X X^3+X^2 X^2+X X+1  1 X^3+X^2+1  1  0 X^3+X^2+X+1  1 X^3+X^2+X  1  1 X^2+X X^3+X^2 X^3+X^2 X^3+X+1 X^3+X^2+1 X^3+X^2+X+1  1  1  1 X^3  1  1 X^3 X^3+X  X X^2+X X^3+X X^2 X^3+X^2+X X^3+X^2+X X^3 X^2 X^3+X X^3+X X^3 X^2  0 X^2 X+1 X^2+X+1  0  1  1 X^2+1  1  1  1 X^3 X^3+X^2+X X^3+X^2+X X^3 X^2
 0  0 X^2 X^2 X^3 X^2 X^3+X^2 X^3+X^2 X^3 X^3  0 X^3+X^2 X^3+X^2  0 X^3+X^2 X^2 X^3  0 X^3+X^2 X^2 X^2 X^3 X^3  0 X^3  0  0 X^3 X^3 X^2 X^3+X^2  0 X^2  0 X^3+X^2 X^2 X^2 X^3 X^3+X^2  0 X^3+X^2 X^3+X^2  0 X^2 X^3 X^3 X^3+X^2 X^3  0 X^2  0 X^3+X^2 X^2 X^3+X^2 X^2 X^3 X^3  0 X^2 X^2  0 X^3 X^3+X^2 X^3+X^2 X^3  0  0 X^2  0 X^3 X^2  0 X^2 X^3+X^2 X^3  0 X^3+X^2 X^3+X^2 X^2 X^2
 0  0  0 X^3  0  0  0 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3  0  0  0  0  0  0 X^3  0  0 X^3  0  0  0  0 X^3 X^3 X^3  0 X^3 X^3  0 X^3 X^3 X^3 X^3  0  0 X^3 X^3 X^3  0  0  0  0  0 X^3 X^3 X^3  0  0  0 X^3 X^3 X^3 X^3  0  0  0  0 X^3 X^3  0 X^3  0  0  0  0 X^3 X^3  0  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+107x^76+192x^77+486x^78+64x^79+428x^80+64x^81+380x^82+192x^83+97x^84+30x^86+1x^88+4x^100+2x^112

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 0.61 seconds.