The generator matrix

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

generates a code of length 4 over Z2[X]/(X^3) who´s minimum homogenous weight is 2.

Homogenous weight enumerator: w(x)=1x^0+14x^2+24x^3+50x^4+24x^5+14x^6+1x^8

The gray image is a linear code over GF(2) with n=16, k=7 and d=4.
This code was found by Heurico 1.16 in 4.79e-005 seconds.