The generator matrix

 1  0  0  0  0  0  1  1  1  1  X  1  1  X  1  1  X  X  1  X  X  1  1  1  1  1
 0  1  0  0  0  0  0  0  0  0  0  0  0  X  X X+1  1  1 X+1  1  1  X X+1  1 X+1  1
 0  0  1  0  0  0  0  0 X+1  1  1  1  X  1  0 X+1  0  X  X X+1 X+1  0  0  0  1  X
 0  0  0  1  0  0  0  1  1  0 X+1  1 X+1 X+1 X+1 X+1 X+1 X+1 X+1  0  0  X  0  X X+1  0
 0  0  0  0  1  0  1  1  0 X+1  1  1  1 X+1  0  X  1 X+1 X+1  0  1  X  X  1  1 X+1
 0  0  0  0  0  1  1  0 X+1  X X+1  1  1  X  0  0 X+1  X  0  1  1 X+1  X  1  X  0
 0  0  0  0  0  0  X  0  X  0  0  0  X  X  X  0  X  X  X  0  X  0  X  0  0  X
 0  0  0  0  0  0  0  X  0  X  X  0  X  0  0  X  0  X  0  X  X  X  X  X  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+88x^17+188x^18+336x^19+545x^20+682x^21+966x^22+1222x^23+1443x^24+1784x^25+1786x^26+1668x^27+1632x^28+1348x^29+1006x^30+680x^31+431x^32+304x^33+146x^34+60x^35+39x^36+18x^37+4x^38+2x^39+5x^40

The gray image is a linear code over GF(2) with n=52, k=14 and d=17.
This code was found by Heurico 1.16 in 16.5 seconds.