The generator matrix

 1  0  1  X  1
 0  1  1  0  0
 0  0  X  X  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+23x^2+44x^3+104x^4+168x^5+104x^6+44x^7+23x^8+1x^10

The gray image is a linear code over GF(2) with n=20, k=9 and d=4.
This code was found by Heurico 1.16 in 0.000145 seconds.