The generator matrix

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

generates a code of length 21 over Z4[X]/(X^2+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 1.05e-007 seconds.