The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+20x^21+4x^22+4x^23+3x^24

The gray image is a code over GF(2) with n=168, k=5 and d=84.
This code was found by Heurico 1.16 in 1.05e-007 seconds.