The generator matrix

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

generates a code of length 80 over Z2[X]/(X^4) who´s minimum homogenous weight is 75.

Homogenous weight enumerator: w(x)=1x^0+110x^75+764x^76+996x^77+1179x^78+994x^79+1013x^80+744x^81+677x^82+586x^83+451x^84+224x^85+202x^86+94x^87+100x^88+28x^89+20x^90+6x^92+1x^94+1x^98+1x^100

The gray image is a linear code over GF(2) with n=640, k=13 and d=300.
This code was found by Heurico 1.16 in 14.2 seconds.