The generator matrix

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

generates a code of length 5 over Z2[X]/(X^3) who´s minimum homogenous weight is 4.

Homogenous weight enumerator: w(x)=1x^0+1x^4+10x^5+2x^6+2x^7

The gray image is a linear code over GF(2) with n=20, k=4 and d=8.
This code was found by Heurico 1.16 in 5.41e-005 seconds.