The generator matrix
1 1 1 1 1
0 X 0 X 0
0 0 X X 0
0 0 0 2 0
generates a code of length 5 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 2.
Homogenous weight enumerator: w(x)=1x^0+39x^2+84x^3+184x^4+1432x^5+184x^6+84x^7+39x^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 6.87e-008 seconds.