The generator matrix

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

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+219x^20+128x^21+336x^22+128x^23+205x^24+5x^28+2x^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 0.016 seconds.