The generator matrix

 1  0  1  1  1 3X+2  1  1 3X  1  1  2  1  1  2  1  1 3X  1  1 3X+2  1  1  0  1  1 2X  1  1 X+2  1  1  X  1  1 2X+2  1  1  1  1 2X X+2  1  1  1  1 2X+2  X  X  X  0  X  X  2  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 2X+2  X  X  1
 0  1 X+1 3X+2 2X+3  1  2 X+3  1 3X 2X+1  1  0 X+1  1 3X+2 2X+3  1  2 X+3  1 3X 2X+1  1 2X 3X+1  1 X+2  3  1 2X+2 3X+3  1  X  1  1 2X X+2 3X+1  3  1  1 2X+2  X 3X+3  1  1  1  0 3X+2  X  2 3X  X  0 2X X+1 3X+1 3X+2 X+2 2X+3  3  2  2 3X 3X X+3 X+3 2X+1 2X+1  0 2X 3X+2 X+2 2X+2 2X+2  X  X X+1 3X+1  0 2X 2X+2  0
 0  0 2X 2X  0 2X 2X  0  0  0 2X 2X 2X  0  0  0 2X 2X  0 2X  0 2X  0 2X 2X 2X 2X  0  0  0  0  0 2X 2X 2X  0  0 2X  0 2X  0 2X 2X  0 2X  0 2X  0 2X 2X 2X 2X 2X 2X  0 2X  0 2X  0 2X  0 2X  0 2X  0 2X  0 2X  0 2X 2X  0 2X  0 2X  0 2X  0 2X  0 2X  0 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+20x^82+268x^83+21x^84+138x^85+8x^86+40x^87+8x^88+2x^89+2x^90+2x^92+1x^98+1x^118

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 0.391 seconds.