The generator matrix

 1  1  1
 0  X X^3
 0  0 X^2

generates a code of length 3 over Z2[X]/(X^4) who´s minimum homogenous weight is 1.

Homogenous weight enumerator: w(x)=1x^0+10x^1+47x^2+396x^3+47x^4+10x^5+1x^6

The gray image is a linear code over GF(2) with n=24, k=9 and d=4.
This code was found by Heurico 1.16 in 1.05e-007 seconds.