The generator matrix
1 1 1 1 1
0 2 0 2 0
0 0 2 2 0
generates a code of length 5 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 4.
Homogenous weight enumerator: w(x)=1x^0+3x^4+24x^5+3x^6+1x^10
The gray image is a code over GF(2) with n=20, k=5 and d=8.
This code was found by Heurico 1.16 in 6.29e-005 seconds.