The generator matrix

 1  1  1  1  1  1  1  1
 0  X  0  0  0  0  0  X
 0  0  X  0  0  0  0  X
 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+28x^4+198x^8+28x^12+1x^16

The gray image is a linear code over GF(2) with n=16, k=8 and d=4.
This code was found by Heurico 1.16 in -5.72e-009 seconds.