The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+212x^22+146x^24+104x^26+28x^28+20x^30+1x^32

The gray image is a code over GF(2) with n=96, k=9 and d=44.
This code was found by Heurico 1.16 in 0.289 seconds.