The generator matrix

 1  1  1
 0  X X^2
 0  0  X

generates a code of length 3 over Z2[X]/(X^3) who´s minimum homogenous weight is 1.

Homogenous weight enumerator: w(x)=1x^0+6x^1+15x^2+84x^3+15x^4+6x^5+1x^6

The gray image is a linear code over GF(2) with n=12, k=7 and d=2.
This code was found by Heurico 1.16 in 9.2e-005 seconds.