The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  1
 0  X X^2+2 X^2+X  0 X^2+X X^2+2 X+2  0 X^2+X X^2+2 X+2  0  2 X^2+X+2 X+2 X^2+X X^2+2  0 X+2  2
 0  0  2  0  0  0  2  2  2  0  0  2  0  2  0  0  2  2  2  0  0
 0  0  0  2  0  0  2  2  0  2  2  2  2  2  0  0  0  2  2  2  2
 0  0  0  0  2  2  0  0  2  2  2  2  0  2  0  2  2  2  0  0  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+89x^18+106x^20+640x^21+114x^22+52x^24+21x^26+1x^40

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 0.032 seconds.