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

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

Homogenous weight enumerator: w(x)=1x^0+84x^81+91x^82+168x^83+92x^84+56x^85+4x^86+8x^87+4x^89+3x^96+1x^114

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 0.625 seconds.