The generator matrix

 1  0  0  0  1
 0  1  0  0  X
 0  0  1  0  0
 0  0  0  1  0
 0  0  0  0  1

generates a code of length 5 over Z2[X]/(X^3) who´s minimum homogenous weight is 1.

Homogenous weight enumerator: w(x)=1x^0+30x^1+365x^2+2280x^3+7570x^4+12276x^5+7570x^6+2280x^7+365x^8+30x^9+1x^10

The gray image is a linear code over GF(2) with n=20, k=15 and d=2.
As d=3 is an upper bound for linear (20,15,2)-codes, this code is optimal over Z2[X]/(X^3) for dimension 15.
This code was found by Heurico 1.16 in 0.109 seconds.