The generator matrix

 1  0  1  1  1  0  1  1  0  1  1  0  1  1  0  1  1  0  X  1  1  1  1  1  1
 0  1  1  0  1  1  0  1  1  0  1  1  0 X+1  1 X+1  0  1  X X+1 X+1 X+1 X+1  0  0
 0  0  X  0  0  0  0  0  0  0  0  0  0  0  0  0  X  X  X  X  X  X  0  0  0
 0  0  0  X  0  0  0  0  0  0  0  0  0  X  X  X  X  X  0  X  X  0  0  0  0
 0  0  0  0  X  0  0  0  0  0  0  0  X  X  X  0  0  0  X  X  X  X  0  0  0
 0  0  0  0  0  X  0  0  0  0  0  0  X  0  X  X  0  X  X  X  0  0  0  0  0
 0  0  0  0  0  0  X  0  0  0  0  X  0  0  X  X  0  X  X  0  X  X  0  0  0
 0  0  0  0  0  0  0  X  0  0  0  X  X  0  0  X  X  X  0  0  X  0  0  0  0
 0  0  0  0  0  0  0  0  X  0  0  X  X  0  X  0  X  X  0  X  0  X  0  0  0
 0  0  0  0  0  0  0  0  0  X  0  X  0  X  X  0  X  0  0  0  X  X  0  0  0
 0  0  0  0  0  0  0  0  0  0  X  0  X  X  0  X  X  0  0  X  0  X  X  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+80x^14+174x^16+348x^18+464x^20+1208x^22+1920x^24+1512x^26+1328x^28+816x^30+113x^32+92x^34+96x^36+40x^38

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 1.33 seconds.