The generator matrix

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

generates a code of length 21 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 17.

Homogenous weight enumerator: w(x)=1x^0+32x^17+134x^18+164x^19+449x^20+514x^21+437x^22+152x^23+120x^24+28x^25+4x^26+4x^27+5x^28+2x^29+1x^30+1x^32

The gray image is a code over GF(2) with n=168, k=11 and d=68.
This code was found by Heurico 1.16 in 0.031 seconds.