The generator matrix

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

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+104x^20+128x^21+584x^22+768x^23+976x^24+768x^25+512x^26+128x^27+96x^28+24x^30+7x^32

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 0.062 seconds.