The generator matrix

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

generates a code of length 22 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 17.

Homogenous weight enumerator: w(x)=1x^0+120x^17+1070x^18+2890x^19+7556x^20+13160x^21+15810x^22+13350x^23+7763x^24+2624x^25+918x^26+238x^27+30x^28+2x^30+2x^31+2x^32

The gray image is a code over GF(2) with n=176, k=16 and d=68.
This code was found by Heurico 1.16 in 9.39 seconds.