The generator matrix

1 0 0 0 0 0 1 1 1 0 1 0 X 0 1 0 1 X X 0 1 0 X 1 1
0 1 0 0 0 0 0 0 1 0 X+1 1 X 1 X 1 X 0 1 X 1 1 1 0 0
0 0 1 0 0 0 0 1 0 X 1 1 1 X X+1 0 X 1 X 1 0 X+1 1 0 0
0 0 0 1 0 0 0 1 1 1 1 X 0 X+1 1 X+1 X+1 1 0 0 X 0 X X 0
0 0 0 0 1 0 1 0 X+1 1 X+1 X+1 1 1 1 0 1 X X X X X 0 0 0
0 0 0 0 0 1 1 X+1 X 1 1 0 X+1 1 1 X 0 1 1 1 X+1 X+1 X+1 0 0
0 0 0 0 0 0 X X 0 X X 0 X 0 0 X X 0 0 X 0 0 0 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+57x^16+371x^18+817x^20+1155x^22+1574x^24+1790x^26+1354x^28+694x^30+272x^32+79x^34+21x^36+7x^38

The gray image is a linear code over GF(2) with n=50, k=13 and d=16.
This code was found by Heurico 1.10 in 0.672 seconds.