The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  X  X  X  1  1  1
 0  X  0  0  0  0  0  0  0  0  0  X  0  0  X  X  X  X  0  0  X  X  0  0  0
 0  0  X  0  0  0  0  0  0  0  0  X  X  X  X  X  0  0  0  0  X  X  X  X  0
 0  0  0  X  0  0  0  0  0  0  X  0  X  X  0  X  X  0  0  X  0  X  X  X  0
 0  0  0  0  X  0  0  0  0  0  X  0  0  X  X  X  0  X  X  X  0  0  0  0  0
 0  0  0  0  0  X  0  0  0  X  0  0  0  X  X  X  X  0  X  0  0  X  0  0  0
 0  0  0  0  0  0  X  0  0  X  0  0  X  0  0  X  X  X  0  X  X  0  X  X  0
 0  0  0  0  0  0  0  X  0  X  X  X  X  0  0  X  0  0  0  0  X  X  0  0  0
 0  0  0  0  0  0  0  0  X  X  X  X  0  0  X  0  0  X  X  0  0  X  X  X  0

generates a code of length 25 over Z2[X]/(X^2) who´s minimum homogenous weight is 16.

Homogenous weight enumerator: w(x)=1x^0+37x^16+24x^18+78x^20+64x^21+48x^22+74x^24+384x^25+73x^26+40x^28+64x^29+68x^30+24x^32+38x^34+2x^36+4x^38+1x^42

The gray image is a linear code over GF(2) with n=50, k=10 and d=16.
This code was found by Heurico 1.16 in 0.0435 seconds.