The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+45x^22+80x^23+261x^24+80x^25+42x^26+2x^28+1x^46

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 0.015 seconds.