The generator matrix

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

generates a code of length 24 over Z4[X]/(X^2+2X+2) 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 0.016 seconds.