The generator matrix
1 1 1 1 1 1 1 1 X 1 1 X X X 2 0 X 2 X 1
0 2 0 2 0 2 0 2 2 0 2 0 2 0 2 2 2 0 0 0
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+1x^20+10x^21+2x^22+2x^23
The gray image is a code over GF(2) with n=80, k=4 and d=40.
This code was found by Heurico 1.16 in 0.00147 seconds.