The generator matrix

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

generates a code of length 16 over Z2[X]/(X^2) who´s minimum homogenous weight is 10.

Homogenous weight enumerator: w(x)=1x^0+51x^10+60x^11+120x^12+188x^13+206x^14+224x^15+265x^16+344x^17+220x^18+156x^19+112x^20+44x^21+34x^22+8x^23+14x^24+1x^26

The gray image is a linear code over GF(2) with n=32, k=11 and d=10.
This code was found by Heurico 1.16 in 0.049 seconds.