The generator matrix

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

generates a code of length 5 over Z2[X]/(X^4) who´s minimum homogenous weight is 3.

Homogenous weight enumerator: w(x)=1x^0+16x^3+98x^4+288x^5+88x^6+16x^7+5x^8

The gray image is a linear code over GF(2) with n=40, k=9 and d=12.
This code was found by Heurico 1.16 in -6.48e-008 seconds.