The generator matrix

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

generates a code of length 20 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 20.

Homogenous weight enumerator: w(x)=1x^0+57x^20+4x^22+1x^24+1x^28

The gray image is a code over GF(2) with n=160, k=6 and d=80.
This code was found by Heurico 1.16 in 1.05e-007 seconds.