The generator matrix
1 1 X 1 1
0 X X+2 0 0
0 0 2X 0 0
0 0 0 2X 0
0 0 0 0 2X
generates a code of length 5 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 2.
Homogenous weight enumerator: w(x)=1x^0+17x^2+206x^4+576x^5+206x^6+17x^8+1x^10
The gray image is a code over GF(2) with n=40, k=10 and d=8.
This code was found by Heurico 1.16 in -6.48e-008 seconds.