The generator matrix

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

generates a code of length 21 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 16.

Homogenous weight enumerator: w(x)=1x^0+328x^16+1838x^17+5660x^18+14550x^19+25260x^20+35112x^21+26405x^22+14548x^23+5213x^24+1702x^25+350x^26+86x^27+14x^28+4x^29+1x^30

The gray image is a code over GF(2) with n=168, k=17 and d=64.
This code was found by Heurico 1.16 in 34 seconds.