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  X  X  1  X  X  X  X  X  1  1  1  1  1  1  X  X  X  X  X  X  X  1  1  1  1  1  1 2X+2 2X+2 2X+2 2X+2 2X+2 2X+2 2X+2  X  X  X  X  X  X  X  X  X  1  1  X 2X  1  1 2X 2X  0 2X  0  0  0 2X+2
 0 2X  0  0  0 2X 2X 2X  0  0  0  0 2X 2X 2X 2X  0  0  0  0 2X 2X 2X 2X  0  0  0 2X 2X  0 2X 2X  0  0  0 2X 2X 2X 2X  0  0  0  0 2X 2X 2X 2X  0  0  0 2X 2X 2X 2X  0  0 2X 2X  0 2X 2X  0  0  0 2X 2X  0 2X 2X  0  0  0  0  0 2X 2X  0 2X 2X 2X 2X  0  0  0
 0  0 2X  0 2X 2X 2X  0  0  0 2X 2X 2X 2X  0  0  0  0 2X 2X 2X 2X  0  0  0  0 2X 2X 2X 2X  0  0  0 2X 2X 2X 2X  0  0  0  0 2X 2X 2X 2X  0  0  0 2X 2X 2X 2X  0  0  0 2X 2X  0 2X 2X  0  0  0 2X 2X  0 2X 2X  0  0  0  0  0 2X 2X 2X 2X  0  0  0  0 2X 2X  0
 0  0  0 2X 2X  0 2X 2X  0 2X 2X  0  0 2X 2X  0  0 2X 2X  0  0 2X 2X  0  0 2X 2X  0 2X  0 2X  0 2X 2X  0  0 2X 2X  0  0 2X 2X  0  0 2X 2X  0 2X 2X  0  0 2X 2X  0 2X 2X  0  0  0 2X 2X  0 2X 2X  0  0  0 2X 2X  0  0 2X  0 2X  0 2X  0 2X  0  0 2X  0 2X  0

generates a code of length 84 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 84.

Homogenous weight enumerator: w(x)=1x^0+116x^84+2x^88+8x^92+1x^96

The gray image is a code over GF(2) with n=672, k=7 and d=336.
This code was found by Heurico 1.16 in 0.406 seconds.