The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+136x^17+962x^18+3304x^19+7110x^20+12720x^21+16718x^22+13312x^23+7223x^24+2920x^25+834x^26+248x^27+40x^28+6x^30+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 9.61 seconds.