The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+156x^19+1192x^20+3512x^21+7669x^22+12428x^23+15241x^24+13082x^25+7834x^26+3012x^27+1034x^28+316x^29+49x^30+4x^31+4x^32+2x^33

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 10.5 seconds.