The generator matrix

 1  0  1  1  1  0  1  1  1  0  1  X  1  1  X  1
 0  1  1  0  1  1  0  X X+1  1  1  1  0  0  X  0
 0  0  X  0  0  X  X  X  0  0  X  X  0  X  X  0
 0  0  0  X  0  X  X  0  X  X  X  0  0  0  0  0
 0  0  0  0  X  X  X  X  X  0  0  X  X  X  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+12x^12+16x^13+7x^14+16x^15+19x^16+16x^17+20x^18+16x^19+4x^22+1x^30

The gray image is a linear code over GF(2) with n=32, k=7 and d=12.
This code was found by Heurico 1.16 in 0.000959 seconds.