The generator matrix

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

generates a code of length 24 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 19.

Homogenous weight enumerator: w(x)=1x^0+228x^19+1117x^20+3808x^21+6890x^22+12740x^23+15587x^24+13184x^25+7232x^26+3532x^27+859x^28+288x^29+50x^30+12x^31+4x^32+4x^34

The gray image is a code over GF(2) with n=192, k=16 and d=76.
This code was found by Heurico 1.16 in 10.3 seconds.