The generator matrix

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

generates a code of length 7 over Z2[X]/(X^2) who´s minimum homogenous weight is 5.

Homogenous weight enumerator: w(x)=1x^0+10x^5+18x^6+14x^7+7x^8+6x^9+6x^10+2x^11

The gray image is a linear code over GF(2) with n=14, k=6 and d=5.
As d=5 is an upper bound for linear (14,6,2)-codes, this code is optimal over Z2[X]/(X^2) for dimension 6.
This code was found by Heurico 1.16 in 0.000125 seconds.