The generator matrix

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

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+490x^18+960x^19+1684x^20+2064x^21+1546x^22+928x^23+453x^24+16x^25+43x^26+6x^28+1x^34

The gray image is a code over GF(2) with n=168, k=13 and d=72.
This code was found by Heurico 1.16 in 78.2 seconds.