The generator matrix

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

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+35x^14+12x^15+138x^16+66x^17+335x^18+432x^19+668x^20+794x^21+1191x^22+1768x^23+1708x^24+2148x^25+1731x^26+1520x^27+1224x^28+996x^29+681x^30+364x^31+325x^32+90x^33+109x^34+28x^36+2x^37+13x^38+4x^40+1x^42

The gray image is a linear code over GF(2) with n=50, k=14 and d=14.
This code was found by Heurico 1.16 in 4.51 seconds.