The generator matrix

 1  0  0  1  1  1  1
 0  1  0  1  X  X  0
 0  0  1  1  1 X+1  0
 0  0  0  X  0  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+16x^4+18x^5+16x^6+30x^7+13x^8+14x^9+16x^10+2x^11+2x^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 0.000187 seconds.