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

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+6x^82+100x^83+6x^84+1x^86+10x^87+1x^88+1x^94+2x^95

The gray image is a linear code over GF(2) with n=664, k=7 and d=328.
This code was found by Heurico 1.16 in 0.61 seconds.