The generator matrix

 1  0  1  1  1 X+2  1  1  2  1  1  X  1  1  1  1  1  1  1  1
 0  1 X+1 X+2  3  1  2 X+3  1  X  1  1  0  2 X+2  X X+1 X+3  3  1

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

Homogenous weight enumerator: w(x)=1x^0+60x^20+2x^24+1x^32

The gray image is a code over GF(2) with n=80, k=6 and d=40.
This code was found by Heurico 1.16 in 0.00113 seconds.