The generator matrix

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

generates a code of length 24 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 24.

Homogenous weight enumerator: w(x)=1x^0+16x^24+10x^25+2x^26+2x^27+1x^28

The gray image is a code over GF(2) with n=192, k=5 and d=96.
This code was found by Heurico 1.16 in 0.016 seconds.