The generator matrix

 1  0  1  1  1  0  1  1  0  1  1  0  1  1  X  1
 0  1  1  0  1  1  0  1  1  0 X+1  1  0  0  0  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  0  X  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  0  X  0
 0  0  0  0  0  0  X  0  0  0  X  X  X  0  0  0
 0  0  0  0  0  0  0  X  0  0  0  X  X  X  0  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  0  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+85x^8+76x^10+64x^11+296x^12+320x^13+320x^14+640x^15+443x^16+640x^17+440x^18+320x^19+184x^20+64x^21+160x^22+15x^24+28x^26

The gray image is a linear code over GF(2) with n=32, k=12 and d=8.
This code was found by Heurico 1.16 in 0.0968 seconds.