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

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+76x^22+80x^23+201x^24+80x^25+68x^26+5x^28+1x^44

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 -1.01e-007 seconds.