The generator matrix

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

generates a code of length 24 over Z4[X]/(X^2+2) 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 10.4 seconds.