The generator matrix
1 1 1 1 1 1 1 1 X X X 1 1 1 1 X 1 1 1 1
0 2 0 2 0 0 2 2 0 2 2 0 0 2 2 0 0 0 2 2
0 0 2 2 0 2 2 0 2 2 0 0 2 2 0 0 0 2 2 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+28x^20+2x^24+1x^32
The gray image is a code over GF(2) with n=80, k=5 and d=40.
This code was found by Heurico 1.16 in 0.00156 seconds.