The generator matrix

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

generates a code of length 16 over Z2[X]/(X^2) who´s minimum homogenous weight is 9.

Homogenous weight enumerator: w(x)=1x^0+28x^9+78x^10+136x^11+206x^12+330x^13+446x^14+518x^15+591x^16+538x^17+442x^18+350x^19+210x^20+126x^21+58x^22+18x^23+16x^24+2x^25+2x^27

The gray image is a linear code over GF(2) with n=32, k=12 and d=9.
This code was found by Heurico 1.16 in 0.162 seconds.