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

generates a code of length 83 over Z2[X]/(X^4) who´s minimum homogenous weight is 82.

Homogenous weight enumerator: w(x)=1x^0+72x^82+128x^83+38x^84+12x^86+4x^98+1x^104

The gray image is a linear code over GF(2) with n=664, k=8 and d=328.
This code was found by Heurico 1.16 in 3.45 seconds.