The generator matrix

 1  0  0  0  1  1  1  1  1  1  1 2X+2  X X+2 3X+2 2X  1  X  1  1 2X  1
 0  1  0  0  0 2X 2X+3 3X+1  1 X+2 X+1  1  1 3X  1  2 3X+2  1 X+3 2X+3 3X+2 X+3
 0  0  1  0  1 X+2 2X+2 3X 3X+3 2X+1 2X+3  1  X  1 2X+1 3X+2  X  2 2X+3 X+2 2X+2  0
 0  0  0  1  1 X+1 3X+3 2X  0 X+2 X+1 2X+3 X+1  3  X  1 2X+2 X+2  3 2X+2  1 2X+3
 0  0  0  0 2X  0  0  0 2X 2X 2X  0 2X  0  0 2X 2X 2X  0  0 2X 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+454x^17+1693x^18+6614x^19+13657x^20+27356x^21+31028x^22+28216x^23+13639x^24+6230x^25+1626x^26+494x^27+47x^28+8x^29+4x^30+4x^31+1x^34

The gray image is a code over GF(2) with n=176, k=17 and d=68.
This code was found by Heurico 1.16 in 37.3 seconds.