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
 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+120x^2+1820x^4+8008x^6+12870x^8+8008x^10+1820x^12+120x^14+1x^16

The gray image is a linear code over GF(2) with n=16, k=15 and d=2.
As d=2 is an upper bound for linear (16,15,2)-codes, this code is optimal over Z2[X]/(X^2) for dimension 15.
This code was found by Heurico 1.16 in 0.823 seconds.