The generator matrix

 1  0  1  1  1 X+2  1  1  0  1  1 X+2 2X  1  1  1  1  1  1  1  1  1  1  1
 0  1 X+1 X+2 2X+3  1 3X+1  0  1 2X+1 X+2  1  1 2X  3 X+3 3X+2  0 X+2 3X+3 2X+2 3X 2X+2  0
 0  0 2X+2  0  0 2X  0 2X+2  2  2 2X+2  2 2X 2X  0 2X  0  2 2X+2  0 2X  2  2 2X
 0  0  0  2 2X 2X+2 2X+2  2  2 2X+2 2X 2X  2  2 2X+2 2X  0  0 2X+2  2 2X+2  2  2  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+40x^20+228x^21+485x^22+802x^23+1011x^24+804x^25+469x^26+200x^27+30x^28+8x^29+4x^30+6x^31+6x^32+1x^34+1x^38

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.