The generator matrix

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

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+164x^8+320x^10+1888x^12+3264x^14+5110x^16+3264x^18+1888x^20+320x^22+164x^24+1x^32

The gray image is a linear code over GF(2) with n=32, k=14 and d=8.
This code was found by Heurico 1.16 in 56 seconds.