The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+20x^1+100x^2+428x^3+2998x^4+428x^5+100x^6+20x^7+1x^8

The gray image is a linear code over GF(2) with n=32, k=12 and d=4.
This code was found by Heurico 1.16 in 3.81e-009 seconds.