The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+25x^20+4x^22+2x^26

The gray image is a code over GF(2) with n=160, k=5 and d=80.
This code was found by Heurico 1.16 in -6.48e-008 seconds.