The generator matrix

 1  1  1  1  1  1  1  1  1  1  X  1  1  X  X  1
 0  X  0  0  0  0  0  0  0  0  0  0  X  X  X  0
 0  0  X  0  0  0  0  0  0  0  0  X  X  X  0  0
 0  0  0  X  0  0  0  0  0  0  0  X  0  X  X  0
 0  0  0  0  X  0  0  0  0  0  0  X  X  0  X  0
 0  0  0  0  0  X  0  0  0  0  X  X  X  X  X  0
 0  0  0  0  0  0  X  0  0  0  X  0  X  0  X  0
 0  0  0  0  0  0  0  X  0  0  X  0  X  X  0  0
 0  0  0  0  0  0  0  0  X  0  X  X  0  X  0  0
 0  0  0  0  0  0  0  0  0  X  X  X  0  0  X  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+77x^8+28x^10+168x^12+128x^13+112x^14+384x^15+203x^16+384x^17+232x^18+128x^19+56x^20+112x^22+7x^24+28x^26

The gray image is a linear code over GF(2) with n=32, k=11 and d=8.
This code was found by Heurico 1.16 in 0.0285 seconds.