The generator matrix
1 1 1 1 X
0 2X+2 0 0 2X+2
0 0 2X+2 0 2
0 0 0 2X+2 2
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+45x^2+338x^4+1280x^5+338x^6+45x^8+1x^10
The gray image is a code over GF(2) with n=40, k=11 and d=8.
This code was found by Heurico 1.16 in 3.62e-008 seconds.