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

generates a code of length 82 over Z2[X]/(X^4) who´s minimum homogenous weight is 77.

Homogenous weight enumerator: w(x)=1x^0+20x^77+99x^78+152x^79+262x^80+350x^81+370x^82+376x^83+179x^84+56x^85+51x^86+64x^87+61x^88+6x^89+1x^156

The gray image is a linear code over GF(2) with n=656, k=11 and d=308.
This code was found by Heurico 1.16 in 0.688 seconds.