The generator matrix

 1  1  1  1  1  1  1  1  X  X  1  X  X  1 X^2  0  1  1 X^2 X^2  1
 0 X^2+2  2 X^2  0 X^2+2  2 X^2 X^2+2 X^2  0  2  0 X^2+2 X^2+2 X^2  2 X^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+19x^20+16x^21+19x^22+8x^23+1x^26

The gray image is a code over GF(2) with n=168, k=6 and d=80.
This code was found by Heurico 1.16 in -6.48e-008 seconds.