The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1
 0  X  0  0  0  0  0  0  0  0  0  0  0  X  X  X
 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  0  X  0  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  X  X  X  X  X
 0  0  0  0  0  0  X  0  0  0  0  X  0  0  X  X
 0  0  0  0  0  0  0  X  0  0  0  X  0  X  X  0
 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  0  0  X
 0  0  0  0  0  0  0  0  0  0  X  X  X  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+140x^8+448x^12+2918x^16+448x^20+140x^24+1x^32

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 7.46 seconds.