The generator matrix

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

generates a code of length 22 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 20.

Homogenous weight enumerator: w(x)=1x^0+222x^20+120x^22+134x^24+8x^26+26x^28+1x^32

The gray image is a code over GF(2) with n=88, k=9 and d=40.
This code was found by Heurico 1.16 in 0.825 seconds.