The generator matrix

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

generates a code of length 26 over Z2[X]/(X^2) who´s minimum homogenous weight is 15.

Homogenous weight enumerator: w(x)=1x^0+52x^15+173x^16+394x^17+749x^18+1190x^19+1792x^20+2646x^21+3780x^22+5048x^23+6074x^24+6984x^25+7386x^26+6984x^27+6360x^28+5184x^29+3816x^30+2800x^31+1852x^32+1118x^33+625x^34+306x^35+128x^36+58x^37+28x^38+4x^39+4x^40

The gray image is a linear code over GF(2) with n=52, k=16 and d=15.
This code was found by Heurico 1.11 in 44 seconds.