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  X  0  1  1  X X^2+2  1  1  1  1  X  0  X X^2+2  X  X  X  2  X  X  X X^2  X X^2  X  2  1  1  X  X  1  X  X  1  1  1  1  1 X^2  1  1  1  1  1  1  1  1  0  0 X^2 X^2  2 X^2  1  1  1  1  1
 0  X X^2+2 X^2+X  0 X^2+X X^2+2 X+2  2 X^2+X+2 X^2 X+2  2 X^2+X+2 X^2  X  0 X^2+X X^2+2 X+2  0 X^2+X X^2+2 X+2  2 X^2+X+2 X^2+X  X X^2  X X+2  X  2 X^2+X+2 X^2  X X^2+X  X X+2  X  0 X^2+2 X^2+X+2  X  2 X^2  X  X X^2+X+2  X  X  X  0 X^2+2  0 X^2+2 X^2+2 X^2  2  0 X^2+X X+2 X^2+X X+2 X^2+2  2  2 X^2 X^2 X^2+X+2 X^2+X+2  X  X X^2 X^2 X^2+2  0  0  2  0  2 X^2+X X^2+X+2  0
 0  0  2  2  2  0  0  2  2  2  0  0  0  0  2  2  0  0  2  2  2  2  0  0  2  2  2  0  0  0  0  2  0  0  2  2  0  2  2  0  2  2  2  0  2  2  0  2  0  0  2  2  0  0  0  0  2  0  0  2  0  2  2  0  2  2  0  2  0  2  0  2  0  0  2  0  2  2  2  0  0  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+6x^82+142x^83+13x^84+36x^85+5x^86+46x^87+2x^88+4x^90+1x^106

The gray image is a code over GF(2) with n=672, k=8 and d=328.
This code was found by Heurico 1.16 in 0.641 seconds.