The generator matrix

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

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+8x^6+24x^7+13x^8+8x^10+8x^11+2x^12

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 0.000161 seconds.