The generator matrix

 1  0  1  1  1  0  1  1  0  1  1  0  0  0  1  1
 0  1  1  0  1  1  0  1  1  0 X+1  1  1  1  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  X  0  0  0
 0  0  0  0  X  0  0  0  0  0  X  X  0  X  0  0
 0  0  0  0  0  X  0  0  0  X  X  0  0  X  0  0
 0  0  0  0  0  0  X  0  0  X  0  0  X  X  0  0
 0  0  0  0  0  0  0  X  0  X  0  X  X  0  0  0
 0  0  0  0  0  0  0  0  X  X  X  X  0  0  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+55x^8+48x^10+246x^12+464x^14+415x^16+464x^18+260x^20+48x^22+41x^24+6x^28

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 0.0217 seconds.