The generator matrix

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

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+130x^18+694x^19+679x^20+1268x^21+500x^22+574x^23+192x^24+48x^25+1x^26+8x^27+1x^30

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.