The generator matrix

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

generates a code of length 14 over Z2[X]/(X^2) who´s minimum homogenous weight is 10.

Homogenous weight enumerator: w(x)=1x^0+30x^10+70x^12+70x^14+47x^16+26x^18+10x^20+2x^22

The gray image is a linear code over GF(2) with n=28, k=8 and d=10.
This code was found by Heurico 1.16 in 0.016 seconds.