The generator matrix

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

generates a code of length 23 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 22.

Homogenous weight enumerator: w(x)=1x^0+299x^22+165x^24+44x^26+2x^28+1x^38

The gray image is a code over GF(2) with n=184, k=9 and d=88.
This code was found by Heurico 1.16 in 75.4 seconds.