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

generates a code of length 82 over Z2[X]/(X^4) who´s minimum homogenous weight is 78.

Homogenous weight enumerator: w(x)=1x^0+194x^78+294x^80+256x^81+588x^82+256x^83+279x^84+138x^86+33x^88+8x^90+1x^156

The gray image is a linear code over GF(2) with n=656, k=11 and d=312.
This code was found by Heurico 1.16 in 0.688 seconds.