The generator matrix

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

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+56x^22+5x^24+2x^28

The gray image is a code over GF(2) with n=176, k=6 and d=88.
This code was found by Heurico 1.16 in 3.62e-008 seconds.