The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  X  1  1  1  X  1  1  X X^2 X^2  X
 0 X^2+2  0 X^2  0  0 X^2 X^2+2  0  2 X^2  2 X^2  2 X^2+2 X^2+2 X^2+2  0 X^2 X^2 X^2+2  2
 0  0 X^2+2 X^2  0 X^2+2 X^2  0  2 X^2  0 X^2  2  0 X^2  2 X^2+2 X^2 X^2 X^2+2  2 X^2+2
 0  0  0  2  2  2  0  2  2  0  2  0  0  0  0  2  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 20.

Homogenous weight enumerator: w(x)=1x^0+122x^20+64x^21+160x^22+64x^23+86x^24+14x^28+1x^32

The gray image is a code over GF(2) with n=176, k=9 and d=80.
This code was found by Heurico 1.16 in 18.4 seconds.