The generator matrix

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

generates a code of length 16 over Z2[X]/(X^2) who´s minimum homogenous weight is 8.

Homogenous weight enumerator: w(x)=1x^0+71x^8+192x^10+470x^12+832x^14+959x^16+832x^18+484x^20+192x^22+57x^24+6x^28

The gray image is a linear code over GF(2) with n=32, k=12 and d=8.
This code was found by Heurico 1.16 in 0.0881 seconds.