The generator matrix

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

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+352x^16+1158x^18+2755x^20+4838x^22+7193x^24+7236x^26+5182x^28+2612x^30+1093x^32+278x^34+63x^36+6x^38+1x^40

The gray image is a linear code over GF(2) with n=50, k=15 and d=16.
This code was found by Heurico 1.16 in 34.9 seconds.