The generator matrix

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

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+36x^2+96x^3+758x^4+96x^5+36x^6+1x^8

The gray image is a linear code over GF(2) with n=32, k=10 and d=8.
This code was found by Heurico 1.16 in 1.05e-007 seconds.