The generator matrix

 1  0  0  0  1  1  1  0  1  1  1  1  X  X  0  X  1  1  1  X  0  1  X  0  1
 0  1  0  0  0  1  1  1  0  X X+1 X+1  1  1  1  1  0  0 X+1  1  X  0  0  1  0
 0  0  1  0  1  1  0  1  0  1  1  0  0  1  X  1 X+1  1  1  1  1  X  1  0  0
 0  0  0  1  1  0  1  1  1  0  1  0  1  0  1  X  0  1 X+1 X+1  0  X  1  0  0
 0  0  0  0  X  0  0  0  0  0  0  X  0  X  X  X  X  0  0  X  X  0  0  0  0
 0  0  0  0  0  X  0  0  0  0  X  0  0  X  0  X  0  X  X  0  0  X  X  X  0
 0  0  0  0  0  0  X  0  0  X  X  X  X  0  X  X  0  X  X  0  0  0  X  X  X
 0  0  0  0  0  0  0  X  0  X  0  0  X  0  X  0  X  X  X  0  0  X  0  X  X
 0  0  0  0  0  0  0  0  X  X  X  X  X  X  0  0  X  0  X  0  0  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+36x^16+70x^17+173x^18+252x^19+337x^20+526x^21+589x^22+708x^23+904x^24+912x^25+902x^26+844x^27+627x^28+480x^29+350x^30+236x^31+131x^32+58x^33+29x^34+8x^35+11x^36+2x^37+5x^38+1x^44

The gray image is a linear code over GF(2) with n=50, k=13 and d=16.
This code was found by Heurico 1.16 in 1.8 seconds.