The generator matrix

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

generates a code of length 21 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 20.

Homogenous weight enumerator: w(x)=1x^0+46x^20+160x^21+46x^22+1x^24+1x^26+1x^34

The gray image is a code over GF(2) with n=168, k=8 and d=80.
This code was found by Heurico 1.16 in -3.24e-008 seconds.