The generator matrix

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

generates a code of length 22 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 21.

Homogenous weight enumerator: w(x)=1x^0+44x^21+164x^22+44x^23+1x^26+1x^28+1x^34

The gray image is a code over GF(2) with n=176, k=8 and d=84.
This code was found by Heurico 1.16 in 0.016 seconds.