The generator matrix

 1  1  1  1  1  1  1  1  X  1  1  X  X  1 X^2  X  X  1 X^2  X  X  X
 0  2  0  2  0  2  0  2  2  0  2  2  0  0  2  0  2  2  0  0  2  0

generates a code of length 22 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 22.

Homogenous weight enumerator: w(x)=1x^0+24x^22+5x^24+2x^28

The gray image is a code over GF(2) with n=176, k=5 and d=88.
This code was found by Heurico 1.16 in 6.87e-008 seconds.