The generator matrix

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

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 0.00219 seconds.