The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+124x^20+248x^21+398x^22+828x^23+1053x^24+700x^25+328x^26+244x^27+111x^28+28x^29+26x^30+6x^32+1x^36

The gray image is a code over GF(2) with n=192, k=12 and d=80.
This code was found by Heurico 1.16 in 0.094 seconds.