The generator matrix

 1  0  1  1  1 3X+2  1  1 2X  1  1 3X  1  1  2  1  1 2X+2 2X  X  1
 0  1 X+1 3X+2  3  1 3X+3 2X  1 3X 2X+3  1  2  1  1 X+2 X+1  1  1  0 2X
 0  0 2X+2  0  2 2X 2X+2  2 2X+2 2X  0 2X  0 2X+2 2X  2  0 2X+2 2X+2  0 2X+2
 0  0  0 2X  0 2X 2X 2X  0 2X 2X  0  0 2X 2X 2X 2X 2X 2X 2X 2X
 0  0  0  0 2X  0 2X  0  0 2X 2X 2X 2X  0 2X  0 2X  0 2X 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+42x^17+158x^18+492x^19+945x^20+878x^21+916x^22+456x^23+135x^24+38x^25+14x^26+12x^27+7x^28+2x^29

The gray image is a code over GF(2) with n=168, k=12 and d=68.
This code was found by Heurico 1.16 in 0.297 seconds.