The generator matrix

 1  0  0  1  1  1  1  1
 0  1  0  1  X X+1  0 X+1
 0  0  1  1  1  0  X X+1
 0  0  0  X  0  X  X  0

generates a code of length 8 over Z2[X]/(X^2) who´s minimum homogenous weight is 6.

Homogenous weight enumerator: w(x)=1x^0+44x^6+45x^8+28x^10+10x^12

The gray image is a linear code over GF(2) with n=16, k=7 and d=6.
As d=6 is an upper bound for linear (16,7,2)-codes, this code is optimal over Z2[X]/(X^2) for dimension 7.
This code was found by Heurico 1.16 in 0.000337 seconds.