The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+12x^1+52x^2+180x^3+534x^4+180x^5+52x^6+12x^7+1x^8

The gray image is a linear code over GF(2) with n=16, k=10 and d=2.
This code was found by Heurico 1.16 in 0.000256 seconds.