The generator matrix

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

generates a code of length 16 over Z2[X]/(X^2) who´s minimum homogenous weight is 11.

Homogenous weight enumerator: w(x)=1x^0+30x^11+96x^12+114x^13+95x^14+112x^15+123x^16+116x^17+117x^18+110x^19+68x^20+26x^21+9x^22+4x^23+3x^26

The gray image is a linear code over GF(2) with n=32, k=10 and d=11.
This code was found by Heurico 1.16 in 0.0242 seconds.