The generator matrix

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

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+81x^22+93x^24+78x^26+1x^30+2x^36

The gray image is a code over GF(2) with n=96, k=8 and d=44.
This code was found by Heurico 1.16 in 0.00514 seconds.