The generator matrix

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

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+110x^16+1014x^17+2692x^18+7220x^19+13310x^20+16870x^21+13218x^22+7400x^23+2635x^24+866x^25+156x^26+36x^27+2x^29+6x^30

The gray image is a code over GF(2) with n=168, k=16 and d=64.
This code was found by Heurico 1.16 in 8.3 seconds.