The generator matrix

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

generates a code of length 26 over Z2[X]/(X^2) who´s minimum homogenous weight is 16.

Homogenous weight enumerator: w(x)=1x^0+73x^16+90x^18+553x^20+810x^22+1657x^24+1796x^26+1719x^28+788x^30+534x^32+98x^34+63x^36+2x^38+7x^40+1x^44

The gray image is a linear code over GF(2) with n=52, k=13 and d=16.
This code was found by Heurico 1.16 in 1.76 seconds.