The generator matrix

 1  0  0  1  1  1  0  1 3X+2  X  1 3X  1 3X  1  1  2 2X  1 3X+2  X 3X+2  1  1
 0  1  0  X 2X+1 3X+3  1  2  1 3X+2 2X+3  1  2  1 X+1 X+2  1  1  0 2X+2  1  1 3X+2 2X+3
 0  0  1  1  1  X 3X+3 2X+1 2X  1 X+1 2X+3  X  X  0 3X+3 3X 3X+1 X+1  1 2X+1 2X+2  3  X
 0  0  0 2X+2  2 2X 2X+2 2X+2  0  2 2X 2X  2 2X+2  2  0  0 2X  2  2  0  2 2X 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+268x^20+892x^21+1972x^22+3320x^23+3621x^24+3212x^25+1920x^26+852x^27+254x^28+40x^29+20x^30+4x^31+8x^32

The gray image is a code over GF(2) with n=192, k=14 and d=80.
This code was found by Heurico 1.16 in 0.813 seconds.