The generator matrix

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

generates a code of length 21 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 18.

Homogenous weight enumerator: w(x)=1x^0+502x^18+936x^19+1712x^20+2012x^21+1632x^22+852x^23+465x^24+36x^25+34x^26+4x^27+6x^28

The gray image is a code over GF(2) with n=168, k=13 and d=72.
This code was found by Heurico 1.16 in 77.1 seconds.