The generator matrix

 1  0  0  1  1  1  0  1  1  1  1  0  X  0  1  1  1  X  1  0  1  1  1  0  1  X
 0  1  0  1  0  1  1  0  0  1  1  1  1  X  0  1  X  1 X+1  1  1 X+1  1  X X+1  X
 0  0  1  1  1  0  1  0  1  1  0  X  1  1  0 X+1  1  1  0  0  1  0  1  1  0  X
 0  0  0  X  0  0  0  0  0  0  0  X  0  X  X  X  0  0  0  0  X  X  0  X  X  X
 0  0  0  0  X  0  0  0  0  0  0  X  X  0  X  0  0  X  0  X  0  X  X  0  0  0
 0  0  0  0  0  X  0  0  0  0  0  0  X  X  X  0  0  X  0  0  X  0  X  0  0  X
 0  0  0  0  0  0  X  0  0  0  0  0  X  0  0  X  X  X  0  0  X  X  X  0  0  0
 0  0  0  0  0  0  0  X  0  0  0  0  0  0  X  0  X  X  X  0  0  X  X  X  0  0
 0  0  0  0  0  0  0  0  X  0  0  X  X  0  X  0  0  X  X  0  X  X  0  0  X  X
 0  0  0  0  0  0  0  0  0  X  0  X  0  X  X  X  X  X  0  X  0  X  X  0  X  X
 0  0  0  0  0  0  0  0  0  0  X  0  X  X  X  0  X  0  0  X  X  X  X  X  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+153x^16+252x^18+1097x^20+1620x^22+3329x^24+3416x^26+3415x^28+1640x^30+1078x^32+236x^34+127x^36+4x^38+15x^40+1x^44

The gray image is a linear code over GF(2) with n=52, k=14 and d=16.
This code was found by Heurico 1.16 in 6.54 seconds.