The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  X  1  1  X  1  1  1  1  1  1  1  1  1
 0  X  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  X  X  X  X  X  X
 0  0  X  0  0  0  0  0  0  0  0  0  0  0  0  0  X  X  X  X  X  X  X  0  0
 0  0  0  X  0  0  0  0  0  0  0  0  0  0  X  X  X  X  0  0  0  X  X  X  X
 0  0  0  0  X  0  0  0  0  0  0  0  0  X  X  X  0  0  X  0  X  X  X  X  0
 0  0  0  0  0  X  0  0  0  0  0  0  0  X  0  X  0  X  X  X  0  0  X  X  0
 0  0  0  0  0  0  X  0  0  0  0  0  0  X  X  0  X  0  0  X  X  0  X  0  0
 0  0  0  0  0  0  0  X  0  0  0  0  X  X  X  X  X  X  X  X  X  X  0  0  0
 0  0  0  0  0  0  0  0  X  0  0  0  X  0  X  0  0  X  X  0  X  0  X  X  0
 0  0  0  0  0  0  0  0  0  X  0  0  X  0  X  X  X  0  X  X  0  0  X  0  X
 0  0  0  0  0  0  0  0  0  0  X  0  X  X  0  X  X  X  0  0  X  0  X  0  X
 0  0  0  0  0  0  0  0  0  0  0  X  X  X  0  0  X  0  X  0  0  X  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+77x^14+242x^16+240x^18+160x^20+520x^22+1024x^23+928x^24+2048x^25+672x^26+1024x^27+320x^28+394x^30+357x^32+112x^34+32x^36+32x^38+8x^40+1x^46

The gray image is a linear code over GF(2) with n=50, k=13 and d=14.
This code was found by Heurico 1.16 in 4.79 seconds.