The generator matrix

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

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+26x^18+178x^19+203x^20+294x^21+140x^22+100x^23+36x^24+30x^25+9x^26+6x^27+1x^30

The gray image is a code over GF(2) with n=168, k=10 and d=72.
This code was found by Heurico 1.16 in 0.016 seconds.