The generator matrix

 1  0  0  0  0  1  1  1  0  1  1  1  1  0  1  1  0  1  0  0  X  X  0  1  1
 0  1  0  0  0  0  0  0  0 X+1  1  1 X+1  1  X  1  1  0  1  X  0  X  0 X+1  0
 0  0  1  0  0  0  1  1  1  1  1 X+1  0 X+1  X  0 X+1  1  1  1  0  1  1  0  0
 0  0  0  1  0  1  1  0  1  0  X  1  1 X+1  0 X+1  X  X  0  1  1 X+1  0 X+1  1
 0  0  0  0  1  1  0  1  1 X+1  X  0 X+1  1 X+1  X  X  X X+1 X+1 X+1  0 X+1  0  1
 0  0  0  0  0  X  0  0  0  X  0  X  0  0  0  X  X  X  0  X  0  X  0  0  0
 0  0  0  0  0  0  X  0  0  0  0  0  0  0  0  0  0  X  X  X  X  X  X  X  0
 0  0  0  0  0  0  0  X  0  0  X  0  0  X  X  X  0  0  0  0  X  X  X  0  0
 0  0  0  0  0  0  0  0  X  0  X  X  X  0  X  X  0  X  0  X  X  0  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+109x^16+140x^17+317x^18+482x^19+718x^20+934x^21+1212x^22+1540x^23+1682x^24+1924x^25+1782x^26+1640x^27+1296x^28+984x^29+692x^30+412x^31+264x^32+112x^33+85x^34+22x^35+26x^36+2x^37+8x^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 13 seconds.