The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  2
 0  X 2X+2 X+2  0 X+2 2X+2 3X  0 X+2 2X+2 3X 2X 3X+2  2 3X  0 2X X+2 3X+2 2X+2 2X+2
 0  0 2X  0  0 2X 2X 2X 2X  0  0  0 2X 2X  0 2X 2X 2X 2X  0 2X  0
 0  0  0 2X 2X 2X 2X  0 2X  0  0 2X  0  0 2X 2X  0 2X  0 2X  0  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+118x^20+276x^22+112x^24+4x^26+1x^40

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 6.87e-008 seconds.