The generator matrix

 1  1  1  1  1  1  1  1  X  0  X 2X  X  2  X 2X+2  1  1  1  1
 0  X  2 3X+2 2X X+2 2X+2 3X 3X+2  X X+2  X 3X  X  X  X  0 2X  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+124x^20+2x^24+1x^32

The gray image is a code over GF(2) with n=160, k=7 and d=80.
This code was found by Heurico 1.16 in 1.05e-007 seconds.