The generator matrix

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

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+18x^4+16x^5+13x^6+32x^7+13x^8+16x^9+18x^10+1x^14

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 0.000178 seconds.