The generator matrix

 1  0  0  0  1  1  1  0  1  1  X  1  1  X  1  1
 0  1  0  0  0  1  1  1  0  X  0  X X+1  1  0  0
 0  0  1  0  1  1  0  1  0  1  1 X+1  0  1  0  0
 0  0  0  1  1  0  1  1  1  0  1  X  0  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  X  X  X  0  0
 0  0  0  0  0  0  X  0  0  X  X  0  X  0  0  0
 0  0  0  0  0  0  0  X  0  X  X  0  0  X  X  X
 0  0  0  0  0  0  0  0  X  0  X  0  X  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+90x^8+230x^10+995x^12+1660x^14+2233x^16+1688x^18+954x^20+260x^22+76x^24+2x^26+3x^28

The gray image is a linear code over GF(2) with n=32, k=13 and d=8.
This code was found by Heurico 1.16 in 0.366 seconds.