The generator matrix

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

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+188x^21+168x^22+464x^23+445x^24+472x^25+144x^26+112x^27+44x^29+8x^30+1x^32+1x^40

The gray image is a code over GF(2) with n=192, k=11 and d=84.
This code was found by Heurico 1.16 in 10.8 seconds.