The generator matrix

 1  0  1  1  1  0  1  1  0  1  1  0  1  1  0  1  1  X  1  0  1  0  1  1  1
 0  1  1  0  1  1  0  1  1  0 X+1  1  0 X+1  1  0  0  0 X+1  1 X+1  1  X  0  0
 0  0  X  0  0  0  0  0  0  0  0  X  0  0  X  X  X  X  0  0  X  X  X  0  0
 0  0  0  X  0  0  0  0  0  0  0  X  X  X  X  X  0  0  X  X  X  X  0  0  0
 0  0  0  0  X  0  0  0  0  X  0  0  X  X  X  0  0  X  0  X  X  0  0  0  0
 0  0  0  0  0  X  0  0  0  X  0  0  0  X  X  X  X  0  X  X  0  0  X  0  0
 0  0  0  0  0  0  X  0  0  0  X  0  0  X  0  X  X  X  0  X  0  X  X  X  0
 0  0  0  0  0  0  0  X  0  X  X  X  X  0  0  X  X  X  0  0  0  0  X  0  0
 0  0  0  0  0  0  0  0  X  X  X  X  X  X  X  0  X  0  X  0  0  X  0  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+23x^16+70x^18+40x^19+105x^20+120x^21+151x^22+200x^23+170x^24+280x^25+161x^26+248x^27+146x^28+104x^29+102x^30+24x^31+62x^32+8x^33+24x^34+5x^36+3x^38+1x^42

The gray image is a linear code over GF(2) with n=50, k=11 and d=16.
This code was found by Heurico 1.16 in 0.126 seconds.