The generator matrix

1 0 0 0 0 0 0 1
0 1 0 0 0 0 0 1
0 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

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+56x^2+924x^4+3976x^6+6470x^8+3976x^10+924x^12+56x^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 1.10 in 0 seconds.