The generator matrix

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

generates a code of length 22 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 20.

Homogenous weight enumerator: w(x)=1x^0+330x^20+384x^22+294x^24+14x^28+1x^32

The gray image is a code over GF(2) with n=176, k=10 and d=80.
This code was found by Heurico 1.16 in 0.032 seconds.