The generator matrix

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

generates a code of length 26 over Z2[X]/(X^2) who´s minimum homogenous weight is 17.

Homogenous weight enumerator: w(x)=1x^0+22x^17+108x^18+162x^19+304x^20+352x^21+453x^22+598x^23+709x^24+888x^25+916x^26+912x^27+764x^28+668x^29+478x^30+344x^31+241x^32+114x^33+88x^34+30x^35+28x^36+4x^37+5x^38+2x^39+1x^40

The gray image is a linear code over GF(2) with n=52, k=13 and d=17.
This code was found by Heurico 1.16 in 2.16 seconds.