The generator matrix

 1  0  1  1  1 3X+2  1  1  2  1  1 3X  1  1  1  1  1  1  1  1  1
 0  1 X+1 3X+2 2X+3  1  2 X+3  1 3X 2X+1  1 2X X+2 2X+2  X 3X+1  3 3X+3  1  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+46x^20+160x^21+46x^22+1x^24+1x^26+1x^34

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 -6.48e-008 seconds.