The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+24x^22+6x^24+1x^32

The gray image is a code over GF(2) with n=88, k=5 and d=44.
This code was found by Heurico 1.16 in 0.00212 seconds.