The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  0  X X^2+2 X^2
 0  X X^2+2 X^2+X  0 X^2+X X^2+2 X+2  2 X^2+X+2 X^2 X+2  2 X^2+X+2 X^2  X X^2+X  X X+2  X  0
 0  0  2  2  2  0  0  2  2  2  0  0  0  0  2  2  0  2  2  0  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+132x^20+112x^22+10x^24+1x^32

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.