The generator matrix

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

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+68x^17+202x^18+394x^19+538x^20+616x^21+936x^22+1276x^23+1466x^24+1676x^25+1806x^26+1796x^27+1594x^28+1340x^29+1002x^30+672x^31+461x^32+240x^33+144x^34+82x^35+36x^36+28x^37+6x^38+4x^39

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 48.1 seconds.