The generator matrix

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

generates a code of length 16 over Z2[X]/(X^2) who´s minimum homogenous weight is 10.

Homogenous weight enumerator: w(x)=1x^0+24x^10+60x^12+104x^14+141x^16+104x^18+44x^20+24x^22+10x^24

The gray image is a linear code over GF(2) with n=32, k=9 and d=10.
This code was found by Heurico 1.16 in 0.126 seconds.