The generator matrix
1 1 1 X 1
0 X 0 2 X+2
0 0 X X X+2
generates a code of length 5 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 3.
Homogenous weight enumerator: w(x)=1x^0+48x^3+162x^4+608x^5+152x^6+48x^7+5x^8
The gray image is a code over GF(2) with n=40, k=10 and d=12.
This code was found by Heurico 1.16 in -1.01e-007 seconds.