The generator matrix

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

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+32x^10+80x^11+134x^12+192x^13+184x^14+224x^15+287x^16+288x^17+256x^18+176x^19+90x^20+32x^21+40x^22+32x^23

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 0.0507 seconds.