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

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

Homogenous weight enumerator: w(x)=1x^0+34x^82+12x^83+1x^84+8x^85+1x^86+4x^87+2x^88+1x^90

The gray image is a linear code over GF(2) with n=656, k=6 and d=328.
This code was found by Heurico 1.16 in 0.36 seconds.