The generator matrix

 1  0  1  1  1  X  X
 0  1  1  X X+1  1  0
 0  0  X  0  X  0  X

generates a code of length 7 over Z2[X]/(X^2) who´s minimum homogenous weight is 6.

Homogenous weight enumerator: w(x)=1x^0+15x^6+15x^8+1x^14

The gray image is a linear code over GF(2) with n=14, k=5 and d=6.
As d=6 is an upper bound for linear (14,5,2)-codes, this code is optimal over Z2[X]/(X^2) for dimension 5.
This code was found by Heurico 1.16 in 0.000128 seconds.