The generator matrix

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

generates a code of length 24 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 22.

Homogenous weight enumerator: w(x)=1x^0+199x^22+210x^23+254x^24+204x^25+103x^26+2x^27+49x^28+2x^34

The gray image is a code over GF(2) with n=192, k=10 and d=88.
This code was found by Heurico 1.16 in 1.05e-007 seconds.