The generator matrix

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

generates a code of length 83 over Z2[X]/(X^4) who´s minimum homogenous weight is 81.

Homogenous weight enumerator: w(x)=1x^0+160x^81+221x^82+348x^83+125x^84+104x^85+33x^86+28x^87+1x^88+1x^98+1x^108+1x^118

The gray image is a linear code over GF(2) with n=664, k=10 and d=324.
This code was found by Heurico 1.16 in 0.609 seconds.