The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  X  1  X  1  1  X  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  X  1  1  1  1 X^3 X^2  X  X X^2  X
 0 X^3+X^2  0 X^2  0  0 X^2 X^3+X^2  0  0 X^2 X^3+X^2  0  0 X^2 X^3+X^2  0  0 X^2 X^3+X^2  0 X^2  0 X^3+X^2  0 X^2 X^3  0 X^3 X^3+X^2 X^3  0 X^2 X^3  0 X^3+X^2 X^3 X^3+X^2 X^3 X^2 X^3 X^3+X^2 X^3 X^2 X^3 X^3+X^2 X^3 X^2 X^3 X^3+X^2 X^3 X^2 X^3 X^3+X^2 X^3 X^2 X^3 X^3+X^2 X^3 X^2 X^3 X^3+X^2 X^3 X^2 X^3 X^3 X^3+X^2 X^2 X^2 X^3+X^2  0 X^3 X^2 X^3+X^2 X^2 X^3+X^2 X^3+X^2 X^3+X^2 X^3 X^3
 0  0 X^3+X^2 X^2  0 X^3+X^2 X^2  0  0 X^3+X^2 X^2  0  0 X^3+X^2 X^2  0 X^3 X^2 X^3+X^2 X^3 X^3 X^3+X^2 X^2 X^3 X^3 X^3+X^2 X^2 X^2 X^2 X^3 X^2 X^3 X^3+X^2 X^3+X^2 X^2 X^3 X^3 X^3+X^2 X^2 X^3 X^3 X^3+X^2 X^3+X^2 X^3 X^2 X^3+X^2  0 X^3 X^3 X^2 X^2  0 X^3 X^2 X^2  0  0 X^2 X^3+X^2  0  0 X^2 X^3+X^2 X^3  0 X^3+X^2 X^3+X^2  0 X^2  0  0 X^3 X^2 X^2 X^3+X^2  0  0 X^3+X^2 X^2 X^3
 0  0  0 X^3  0  0 X^3  0 X^3 X^3  0 X^3 X^3 X^3  0 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  0  0  0  0  0  0 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 X^3 X^3  0 X^3 X^3 X^3  0  0  0  0 X^3 X^3  0  0 X^3 X^3  0  0
 0  0  0  0 X^3 X^3 X^3 X^3 X^3 X^3  0 X^3  0  0 X^3  0  0  0  0  0 X^3 X^3 X^3 X^3 X^3 X^3  0 X^3 X^3 X^3 X^3  0  0  0  0  0  0  0  0  0 X^3 X^3 X^3 X^3 X^3 X^3  0  0 X^3  0  0 X^3  0 X^3 X^3  0  0 X^3  0 X^3 X^3  0  0 X^3 X^3 X^3  0  0  0  0  0 X^3 X^3  0  0 X^3 X^3 X^3 X^3  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+38x^76+96x^77+56x^78+256x^79+61x^80+368x^81+64x^82+32x^83+26x^84+16x^85+8x^86+1x^88+1x^136

The gray image is a linear code over GF(2) with n=640, k=10 and d=304.
This code was found by Heurico 1.16 in 0.578 seconds.