The generator matrix

 1  0  1  1  1  0  1  1  0  1  1  0  1  1  X  X
 0  1  1  0  1  1  0 X+1  1  0 X+1  1  0  X  X  0
 0  0  X  0  0  0  0  X  0  X  X  X  0  X  0  0
 0  0  0  X  0  0  X  X  0  X  0  X  0  0  X  0
 0  0  0  0  X  0  X  0  X  X  X  X  0  0  0  0
 0  0  0  0  0  X  0  X  X  X  0  X  X  0  0  0

generates a code of length 16 over Z2[X]/(X^2) who´s minimum homogenous weight is 12.

Homogenous weight enumerator: w(x)=1x^0+56x^12+20x^14+93x^16+40x^18+40x^20+4x^22+2x^24

The gray image is a linear code over GF(2) with n=32, k=8 and d=12.
This code was found by Heurico 1.16 in -5.72e-009 seconds.