The generator matrix

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

generates a code of length 25 over Z2[X]/(X^2) who´s minimum homogenous weight is 14.

Homogenous weight enumerator: w(x)=1x^0+93x^14+168x^15+429x^16+692x^17+1217x^18+1906x^19+2662x^20+3904x^21+4987x^22+6298x^23+6904x^24+7216x^25+6914x^26+5764x^27+5100x^28+4024x^29+2875x^30+1820x^31+1216x^32+764x^33+293x^34+170x^35+70x^36+40x^37+5x^38+2x^39+2x^40

The gray image is a linear code over GF(2) with n=50, k=16 and d=14.
This code was found by Heurico 1.11 in 36.3 seconds.