The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+20x^23+4x^24+4x^25+2x^26+1x^28

The gray image is a code over GF(2) with n=184, k=5 and d=92.
This code was found by Heurico 1.16 in -1.01e-007 seconds.