The generator matrix

 1  0  0  1  1  1  0  X
 0  1  0  0  1  1  1  0
 0  0  1  1  1  0  1  0
 0  0  0  X  0  0  0  X
 0  0  0  0  X  0  0  X
 0  0  0  0  0  X  0  X
 0  0  0  0  0  0  X  X

generates a code of length 8 over Z2[X]/(X^2) who´s minimum homogenous weight is 4.

Homogenous weight enumerator: w(x)=1x^0+84x^4+224x^6+406x^8+224x^10+84x^12+1x^16

The gray image is a linear code over GF(2) with n=16, k=10 and d=4.
As d=4 is an upper bound for linear (16,10,2)-codes, this code is optimal over Z2[X]/(X^2) for dimension 10.
This code was found by Heurico 1.16 in 0.00184 seconds.