The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+178x^19+517x^20+676x^21+996x^22+1040x^23+1329x^24+1138x^25+1027x^26+626x^27+439x^28+168x^29+40x^30+12x^31+2x^32+2x^33+1x^42

The gray image is a code over GF(2) with n=96, k=13 and d=38.
This code was found by Heurico 1.16 in 0.787 seconds.