The generator matrix

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

generates a code of length 26 over Z2[X]/(X^2) who´s minimum homogenous weight is 16.

Homogenous weight enumerator: w(x)=1x^0+37x^16+104x^17+221x^18+254x^19+416x^20+722x^21+1016x^22+1168x^23+1441x^24+1840x^25+1823x^26+1852x^27+1664x^28+1172x^29+880x^30+736x^31+482x^32+248x^33+147x^34+86x^35+48x^36+10x^37+8x^38+7x^40+1x^42

The gray image is a linear code over GF(2) with n=52, k=14 and d=16.
This code was found by Heurico 1.16 in 12.8 seconds.