The generator matrix

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

generates a code of length 24 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 19.

Homogenous weight enumerator: w(x)=1x^0+188x^19+1163x^20+3560x^21+7230x^22+13280x^23+14453x^24+13764x^25+7252x^26+3228x^27+1085x^28+272x^29+46x^30+8x^31+2x^32+4x^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 10.4 seconds.