The generator matrix

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

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+21x^6+25x^8+10x^10+6x^12+1x^14

The gray image is a linear code over GF(2) with n=16, k=6 and d=6.
As d=6 is an upper bound for linear (16,6,2)-codes, this code is optimal over Z2[X]/(X^2) for dimension 6.
This code was found by Heurico 1.16 in 0.000222 seconds.