The generator matrix

 1  0  1  1  1  0  1  1  0  1  1  0  1  1  0  0
 0  1  1  0  1  1  0  1  1  0 X+1  1  0 X+1  1  1
 0  0  X  0  0  0  0  0  0  0  X  X  X  X  0  0
 0  0  0  X  0  0  0  0  0  X  X  X  0  0  0  X
 0  0  0  0  X  0  0  0  X  X  0  X  0  X  X  X
 0  0  0  0  0  X  0  0  X  X  0  X  X  0  X  0
 0  0  0  0  0  0  X  0  X  0  X  0  X  X  0  X
 0  0  0  0  0  0  0  X  X  X  X  0  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+28x^10+16x^11+68x^12+80x^13+100x^14+160x^15+125x^16+160x^17+100x^18+80x^19+52x^20+16x^21+28x^22+10x^24

The gray image is a linear code over GF(2) with n=32, k=10 and d=10.
This code was found by Heurico 1.16 in 0.472 seconds.