The generator matrix

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

generates a code of length 26 over Z2[X]/(X^2) who´s minimum homogenous weight is 14.

Homogenous weight enumerator: w(x)=1x^0+45x^14+161x^16+104x^17+372x^18+464x^19+932x^20+1256x^21+1927x^22+2624x^23+2953x^24+3792x^25+3514x^26+3680x^27+3082x^28+2576x^29+1915x^30+1344x^31+934x^32+456x^33+368x^34+80x^35+112x^36+8x^37+49x^38+15x^40+2x^42+2x^44

The gray image is a linear code over GF(2) with n=52, k=15 and d=14.
This code was found by Heurico 1.16 in 14.7 seconds.