The generator matrix

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

generates a code of length 8 over Z2[X]/(X^2) who´s minimum homogenous weight is 2.

Homogenous weight enumerator: w(x)=1x^0+68x^2+48x^3+628x^4+880x^5+1980x^6+3168x^7+2838x^8+3168x^9+1980x^10+880x^11+628x^12+48x^13+68x^14+1x^16

The gray image is a linear code over GF(2) with n=16, k=14 and d=2.
As d=2 is an upper bound for linear (16,14,2)-codes, this code is optimal over Z2[X]/(X^2) for dimension 14.
This code was found by Heurico 1.16 in 0.33 seconds.