The generator matrix

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

generates a code of length 21 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 17.

Homogenous weight enumerator: w(x)=1x^0+184x^17+767x^18+2006x^19+3100x^20+4136x^21+3436x^22+1888x^23+593x^24+220x^25+35x^26+10x^27+2x^28+4x^29+2x^30

The gray image is a code over GF(2) with n=168, k=14 and d=68.
This code was found by Heurico 1.16 in 0.625 seconds.