The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+162x^4+192x^5+152x^6+5x^8

The gray image is a linear code over GF(2) with n=40, k=9 and d=16.
As d=16 is an upper bound for linear (40,9,2)-codes, this code is optimal over Z2[X]/(X^4) for dimension 9.
This code was found by Heurico 1.16 in 3.62e-008 seconds.