The generator matrix

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

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+76x^2+192x^3+1510x^4+192x^5+76x^6+1x^8

The gray image is a linear code over GF(2) with n=32, k=11 and d=8.
This code was found by Heurico 1.16 in 3.62e-008 seconds.