The generator matrix

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

generates a code of length 24 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 20.

Homogenous weight enumerator: w(x)=1x^0+457x^20+724x^21+2154x^22+2804x^23+3843x^24+3304x^25+1964x^26+776x^27+263x^28+68x^29+10x^30+4x^31+12x^32

The gray image is a code over GF(2) with n=192, k=14 and d=80.
This code was found by Heurico 1.16 in 0.766 seconds.