The generator matrix

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

generates a code of length 16 over Z2[X]/(X^2) who´s minimum homogenous weight is 9.

Homogenous weight enumerator: w(x)=1x^0+54x^9+174x^10+282x^11+395x^12+642x^13+896x^14+1034x^15+1147x^16+1118x^17+920x^18+670x^19+420x^20+230x^21+120x^22+62x^23+20x^24+4x^25+2x^26+1x^28

The gray image is a linear code over GF(2) with n=32, k=13 and d=9.
This code was found by Heurico 1.16 in 0.691 seconds.