The generator matrix

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

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+240x^22+60x^24+192x^26+16x^30+3x^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 0.00869 seconds.