The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+53x^20+562x^21+997x^22+1426x^23+2231x^24+1368x^25+913x^26+508x^27+81x^28+30x^29+9x^30+10x^31+2x^32+1x^34

The gray image is a code over GF(2) with n=192, k=13 and d=80.
This code was found by Heurico 1.16 in 0.203 seconds.