The generator matrix

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

generates a code of length 21 over Z4[X]/(X^2+2X+2) 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 3.62e-008 seconds.