The generator matrix

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

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+97x^16+154x^17+314x^18+498x^19+637x^20+992x^21+1346x^22+1492x^23+1574x^24+1792x^25+1948x^26+1688x^27+1234x^28+1020x^29+668x^30+396x^31+264x^32+134x^33+74x^34+22x^35+33x^36+4x^37+2x^38

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 15 seconds.