The generator matrix
1 0 1 1 1
0 1 X+1 0 0
0 0 X^2 0 0
0 0 0 X^2 0
generates a code of length 5 over Z2[X]/(X^3) who´s minimum homogenous weight is 2.
Homogenous weight enumerator: w(x)=1x^0+15x^2+64x^4+96x^5+64x^6+15x^8+1x^10
The gray image is a linear code over GF(2) with n=20, k=8 and d=4.
This code was found by Heurico 1.16 in 7.8e-005 seconds.