The generator matrix

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

generates a code of length 84 over Z4[X]/(X^3+2,2X) 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.