The generator matrix

 1  1  1  1  1  1  1  1
 0  X  0  0  0  0  0  0
 0  0  X  0  0  0  0  0
 0  0  0  X  0  0  0  0
 0  0  0  0  X  0  0  0
 0  0  0  0  0  X  0  0
 0  0  0  0  0  0  X  0
 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+8x^2+28x^4+56x^6+326x^8+56x^10+28x^12+8x^14+1x^16

The gray image is a linear code over GF(2) with n=16, k=9 and d=2.
This code was found by Heurico 1.16 in -3.24e-008 seconds.