The generator matrix

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

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+59x^4+136x^5+58x^6+2x^8

The gray image is a linear code over GF(2) with n=40, k=8 and d=16.
As d=16 is an upper bound for linear (40,8,2)-codes, this code is optimal over Z2[X]/(X^4) for dimension 8.
This code was found by Heurico 1.16 in 3.62e-008 seconds.