The generator matrix

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

generates a code of length 24 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 21.

Homogenous weight enumerator: w(x)=1x^0+92x^21+366x^22+366x^23+509x^24+296x^25+257x^26+106x^27+33x^28+17x^30+4x^31+1x^32

The gray image is a code over GF(2) with n=192, k=11 and d=84.
This code was found by Heurico 1.16 in 0.016 seconds.