The generator matrix

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

generates a code of length 80 over Z2[X]/(X^4) who´s minimum homogenous weight is 77.

Homogenous weight enumerator: w(x)=1x^0+480x^77+224x^78+326x^79+109x^80+312x^81+136x^82+332x^83+25x^84+76x^85+14x^86+6x^87+4x^89+1x^100+1x^102+1x^110

The gray image is a linear code over GF(2) with n=640, k=11 and d=308.
This code was found by Heurico 1.16 in 36.6 seconds.