The generator matrix

 1  0  0  0  1  1  1  0  1  1  1  1  X  X  X  1  1  X  X  1  0  1  1  1  0
 0  1  0  0  0  1  1  1  0  0 X+1 X+1  1  0  1  X  X  0  1  1  1 X+1  X X+1  1
 0  0  1  0  1  1  0  1  0  1  1  0  0  1  1  1 X+1  1  0  X  1 X+1  X  1  0
 0  0  0  1  1  0  1  1  1  0  1  0  1  1  0 X+1  X X+1  1  1 X+1 X+1  X  0  X
 0  0  0  0  X  0  0  0  0  0  0  0  0  0  0  X  0  X  X  X  X  X  0  X  0
 0  0  0  0  0  X  0  0  0  0  0  X  0  X  X  0  X  X  0  0  X  0  0  X  0
 0  0  0  0  0  0  X  0  0  0  X  X  0  X  X  0  X  X  X  X  X  X  X  0  0
 0  0  0  0  0  0  0  X  0  0  X  0  X  0  X  X  X  X  X  0  0  0  0  X  X
 0  0  0  0  0  0  0  0  X  0  X  X  X  X  0  X  X  X  0  X  0  0  0  0  X
 0  0  0  0  0  0  0  0  0  X  0  0  0  0  X  0  X  0  X  X  X  0  X  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+173x^16+570x^18+1426x^20+2300x^22+3763x^24+3436x^26+2772x^28+1232x^30+526x^32+138x^34+42x^36+4x^38+1x^40

The gray image is a linear code over GF(2) with n=50, k=14 and d=16.
This code was found by Heurico 1.16 in 12.7 seconds.