The generator matrix

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

generates a code of length 24 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 19.

Homogenous weight enumerator: w(x)=1x^0+490x^19+2415x^20+6876x^21+14794x^22+24848x^23+31177x^24+26338x^25+15294x^26+6058x^27+2001x^28+640x^29+102x^30+28x^31+6x^32+2x^33+2x^34

The gray image is a code over GF(2) with n=192, k=17 and d=76.
This code was found by Heurico 1.16 in 40.7 seconds.