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.