The generator matrix

 1  0  0  1  1  1 X^2+X+2  2  1  1  2  1  1  1 X^2+2 X^2+X  1  1  1  1  1
 0  1  0  1  X X^2+X+1  1  1  X X+2  1 X^2+X+3  1 X^2+2  X  1 X^2+X+3 X^2+X X+2 X^2+X+2  0
 0  0  1  1  1  0  1  X X+1  2 X^2+1 X^2+X+1 X+2 X+2  1 X^2+2 X^2 X^2+X+2  0 X^2+X+1  2
 0  0  0  X  2 X+2 X^2+X X^2+X  X X^2+X X^2 X^2  0 X+2 X+2 X+2 X^2+X+2 X^2+2  2 X^2+X+2  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+87x^16+434x^17+1584x^18+3136x^19+6712x^20+8702x^21+6970x^22+3216x^23+1388x^24+366x^25+148x^26+16x^27+4x^28+2x^29+2x^30

The gray image is a code over GF(2) with n=168, k=15 and d=64.
This code was found by Heurico 1.16 in 2.25 seconds.