The generator matrix

 1  1  X  1
 0 X^3+X^2 X^3+X^2  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+6x^2+16x^3+82x^4+16x^5+6x^6+1x^8

The gray image is a linear code over GF(2) with n=32, k=7 and d=8.
This code was found by Heurico 1.16 in -3.24e-008 seconds.