The generator matrix

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

generates a code of length 22 over Z4[X]/(X^2+2) 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 18.1 seconds.