The generator matrix
1 1 1 1 1
0 2 0 0 0
0 0 2 0 0
0 0 0 2 0
0 0 0 0 2
generates a code of length 5 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 2.
Homogenous weight enumerator: w(x)=1x^0+5x^2+10x^4+96x^5+10x^6+5x^8+1x^10
The gray image is a code over GF(2) with n=20, k=7 and d=4.
This code was found by Heurico 1.16 in 5.79e-005 seconds.