The generator matrix

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

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+30x^18+156x^19+257x^20+216x^21+210x^22+66x^23+38x^24+36x^25+7x^26+6x^27+1x^30

The gray image is a code over GF(2) with n=168, k=10 and d=72.
This code was found by Heurico 1.16 in 3.62e-008 seconds.