The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+14x^2+40x^3+146x^4+40x^5+14x^6+1x^8

The gray image is a linear code over GF(2) with n=32, k=8 and d=8.
This code was found by Heurico 1.16 in 6.87e-008 seconds.