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

generates a code of length 80 over Z2[X]/(X^4) who´s minimum homogenous weight is 74.

Homogenous weight enumerator: w(x)=1x^0+54x^74+101x^76+16x^77+146x^78+352x^79+708x^80+400x^81+142x^82+53x^84+38x^86+30x^88+4x^90+2x^92+1x^152

The gray image is a linear code over GF(2) with n=640, k=11 and d=296.
This code was found by Heurico 1.16 in 0.672 seconds.