The generator matrix

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

generates a code of length 7 over Z2[X]/(X^2) who´s minimum homogenous weight is 4.

Homogenous weight enumerator: w(x)=1x^0+21x^4+32x^6+67x^8+7x^12

The gray image is a linear code over GF(2) with n=14, k=7 and d=4.
As d=4 is an upper bound for linear (14,7,2)-codes, this code is optimal over Z2[X]/(X^2) for dimension 7.
This code was found by Heurico 1.16 in 0.000199 seconds.