The generator matrix

 1  0  0  0  1  1  1  0  1  1  X  1  1  0  X  1
 0  1  0  0  0  1  1  1  0  0  0 X+1 X+1  1  1  0
 0  0  1  0  1  1  0  1  0  1  1  1  0  X  1  0
 0  0  0  1  1  0  1  1  1  0  1  1  X  1  0  0
 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  X  0  X  X  0  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  X  X  X  X  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+109x^8+48x^9+508x^10+560x^11+728x^12+1008x^13+1904x^14+2800x^15+1883x^16+1680x^17+1352x^18+1680x^19+1288x^20+336x^21+304x^22+80x^23+87x^24+28x^26

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 2.37 seconds.