The generator matrix

 1  0  1  1 3X+2  1  1  1 2X+2  1  1 3X  1  0  1  1  X 2X  1 2X+2 3X
 0  1  1 3X+2  1 3X+1  3 2X+2  1  X X+3  1 2X+2  1 3X+1 3X+2 3X  1 2X+3  1  1
 0  0  X  0 2X 2X+2  2 3X 3X  X X+2 3X+2 3X+2 3X+2  X X+2 3X+2 2X+2 3X+2 X+2 X+2
 0  0  0 2X 2X  0 2X  0  0 2X 2X 2X  0  0  0  0  0 2X  0 2X 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+196x^18+572x^19+857x^20+936x^21+808x^22+512x^23+143x^24+24x^25+36x^26+4x^27+7x^28

The gray image is a code over GF(2) with n=168, k=12 and d=72.
This code was found by Heurico 1.16 in 0.047 seconds.