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

generates a code of length 83 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 81.

Homogenous weight enumerator: w(x)=1x^0+100x^81+43x^82+244x^83+12x^84+96x^85+4x^86+4x^87+2x^88+2x^89+1x^90+1x^104+2x^105

The gray image is a code over GF(2) with n=664, k=9 and d=324.
This code was found by Heurico 1.16 in 16.1 seconds.