The generator matrix

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

generates a code of length 24 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 21.

Homogenous weight enumerator: w(x)=1x^0+166x^21+739x^22+658x^23+1168x^24+514x^25+564x^26+178x^27+78x^28+16x^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.