The generator matrix

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

generates a code of length 24 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 22.

Homogenous weight enumerator: w(x)=1x^0+70x^22+180x^23+119x^24+24x^25+56x^26+52x^27+8x^28+1x^30+1x^38

The gray image is a code over GF(2) with n=192, k=9 and d=88.
This code was found by Heurico 1.16 in -6.48e-008 seconds.