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

generates a code of length 85 over Z2[X]/(X^4) who´s minimum homogenous weight is 81.

Homogenous weight enumerator: w(x)=1x^0+142x^81+133x^82+194x^83+313x^84+522x^85+346x^86+160x^87+68x^88+86x^89+33x^90+46x^91+1x^92+2x^93+1x^160

The gray image is a linear code over GF(2) with n=680, k=11 and d=324.
This code was found by Heurico 1.16 in 0.781 seconds.