The generator matrix

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

generates a code of length 21 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 18.

Homogenous weight enumerator: w(x)=1x^0+109x^18+762x^19+539x^20+1458x^21+377x^22+624x^23+144x^24+66x^25+10x^26+2x^27+4x^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.