The generator matrix

 1  0  1  1  1
 0  1  1  0  0
 0  0  X  0 X^2
 0  0  0  X X^2

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+25x^2+40x^3+230x^4+432x^5+230x^6+40x^7+25x^8+1x^10

The gray image is a linear code over GF(2) with n=20, k=10 and d=4.
This code was found by Heurico 1.16 in 0.000336 seconds.