The generator matrix

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

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+24x^3+194x^4+592x^5+184x^6+24x^7+5x^8

The gray image is a linear code over GF(2) with n=40, k=10 and d=12.
This code was found by Heurico 1.16 in 0.016 seconds.