The generator matrix

 1  0  0  1  1  1  1  1
 0  1  0  1  0  0  0  0
 0  0  1  1  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+20x^2+100x^4+428x^6+950x^8+428x^10+100x^12+20x^14+1x^16

The gray image is a linear code over GF(2) with n=16, k=11 and d=2.
This code was found by Heurico 1.16 in 0.0033 seconds.