The generator matrix

 1  0  0  1  1  1  2  1  1 X+2  1 2X  0  1  2  1 3X 3X+2  1 3X  1  X  1  1
 0  1  0 2X+2 2X+3  1  1  2  X  1 X+1  1 3X+2 3X+3  1 3X+2 X+2  1 X+2  1  3  1 2X 2X
 0  0  1 3X+3 X+1 2X+2 X+1 3X 2X+1 3X+3 2X+3  X  1 3X+2 2X+3 2X  1 2X+1 3X+3 3X+3 3X+2  0  3  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+132x^21+716x^22+826x^23+1119x^24+416x^25+539x^26+246x^27+79x^28+8x^29+9x^30+4x^31+1x^32

The gray image is a code over GF(2) with n=192, k=12 and d=84.
This code was found by Heurico 1.16 in 0.047 seconds.