The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+8x^3+34x^4+48x^5+24x^6+8x^7+5x^8

The gray image is a linear code over GF(2) with n=20, k=7 and d=6.
This code was found by Heurico 1.16 in 7.39e-005 seconds.