The generator matrix

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

generates a code of length 23 over Z4[X]/(X^2+2) 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 74.8 seconds.