The generator matrix

 1  0  0  1  X
 0  1  0  1 X^2
 0  0  1  1  0
 0  0  0  X  X
 0  0  0  0 X^2

generates a code of length 5 over Z2[X]/(X^3) who´s minimum homogenous weight is 2.

Homogenous weight enumerator: w(x)=1x^0+93x^2+288x^3+1058x^4+1216x^5+1058x^6+288x^7+93x^8+1x^10

The gray image is a linear code over GF(2) with n=20, k=12 and d=4.
As d=4 is an upper bound for linear (20,12,2)-codes, this code is optimal over Z2[X]/(X^3) for dimension 12.
This code was found by Heurico 1.16 in 0.00333 seconds.