The generator matrix

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

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+386x^76+552x^77+583x^78+384x^79+506x^80+392x^81+459x^82+384x^83+272x^84+64x^85+65x^86+8x^88+8x^89+9x^90+4x^92+8x^93+4x^94+5x^96+1x^100+1x^116

The gray image is a linear code over GF(2) with n=640, k=12 and d=304.
This code was found by Heurico 1.16 in 0.797 seconds.