The generator matrix

 1  1  1  1  1  1  1  1  1  1  X  1  0  X  1 X^2+2  X  X X^2+2  X  X  0  2
 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 X+2 X^2  X X^2 X^2+X  X  0 X^2+X+2 X^2  X
 0  0  2  2  2  0  0  2  2  0  0  0  2  2  2  0  2  2  2  2  2  2  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+150x^22+78x^24+24x^26+2x^30+1x^32

The gray image is a code over GF(2) with n=184, k=8 and d=88.
This code was found by Heurico 1.16 in 0.078 seconds.