The generator matrix

 1  1  1  1  1  1  1  1  X  X  1  1  1  1  X X^2+2  1  X  1  1  1
 0  X  0  X  2  0 X^2+X X^2+X+2 X^2  X X^2+2  0 X^2+X X^2+X+2 X^2+X+2  X X^2+2 X^2+X+2  0 X^2+X+2  X
 0  0  X  X  0 X^2+X+2 X^2+X  2  X X^2+X X+2 X^2+2 X^2+2 X+2  X X^2+2 X^2+X+2 X^2 X^2+X X^2 X^2+X
 0  0  0 X^2 X^2+2 X^2  2 X^2  0 X^2 X^2+2  2 X^2 X^2  2 X^2+2 X^2+2  2  0  0 X^2+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+104x^17+187x^18+470x^19+784x^20+1068x^21+762x^22+404x^23+166x^24+120x^25+19x^26+6x^27+4x^29+1x^32

The gray image is a code over GF(2) with n=168, k=12 and d=68.
This code was found by Heurico 1.16 in 0.078 seconds.