The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  1  X  1  1  1  X  1
 0  X  0  0  0  0  0  0  0  0  0  0  0  0  X  0  0  0  X  X  X  X  X  0  X
 0  0  X  0  0  0  0  0  0  0  0  0  0  0  X  0  X  X  X  0  X  0  X  X  0
 0  0  0  X  0  0  0  0  0  0  0  0  0  X  0  0  X  X  X  X  0  X  X  0  0
 0  0  0  0  X  0  0  0  0  0  0  0  0  X  0  X  0  X  X  0  X  X  0  0  X
 0  0  0  0  0  X  0  0  0  0  0  0  X  0  0  X  0  X  X  0  0  X  X  X  0
 0  0  0  0  0  0  X  0  0  0  0  0  X  0  0  0  X  0  0  X  X  X  X  X  0
 0  0  0  0  0  0  0  X  0  0  0  X  0  0  0  0  X  0  X  X  0  0  X  X  X
 0  0  0  0  0  0  0  0  X  0  0  X  0  0  0  X  0  0  0  X  X  X  0  X  X
 0  0  0  0  0  0  0  0  0  X  0  X  X  X  X  X  X  0  X  X  X  0  X  0  X
 0  0  0  0  0  0  0  0  0  0  X  X  X  X  X  0  0  0  0  0  X  X  X  0  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+190x^16+361x^20+256x^22+1382x^24+768x^26+831x^28+245x^32+55x^36+6x^40+1x^44

The gray image is a linear code over GF(2) with n=50, k=12 and d=16.
This code was found by Heurico 1.16 in 20.7 seconds.