The generator matrix

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

generates a code of length 21 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 16.

Homogenous weight enumerator: w(x)=1x^0+272x^16+1946x^17+5528x^18+14548x^19+26003x^20+34006x^21+26680x^22+14776x^23+5163x^24+1734x^25+336x^26+52x^27+17x^28+10x^29

The gray image is a code over GF(2) with n=168, k=17 and d=64.
This code was found by Heurico 1.16 in 34.8 seconds.