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

generates a code of length 84 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 82.

Homogenous weight enumerator: w(x)=1x^0+109x^82+40x^83+239x^84+16x^85+85x^86+8x^87+6x^88+3x^94+1x^96+1x^98+1x^100+2x^102

The gray image is a code over GF(2) with n=672, k=9 and d=328.
This code was found by Heurico 1.16 in 1.56 seconds.