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

generates a code of length 84 over Z2[X]/(X^4) who´s minimum homogenous weight is 84.

Homogenous weight enumerator: w(x)=1x^0+35x^84+12x^85+2x^86+7x^88+4x^89+2x^90+1x^92

The gray image is a linear code over GF(2) with n=672, k=6 and d=336.
This code was found by Heurico 1.16 in 0.406 seconds.