The generator matrix

 1  0  1  1  1  0  1  1  0  1  1  0  1  1  1  0  X  1  1  X  1  1  1  X  1  1
 0  1  1  0  1  1  0  1  1  0  1  1  0  X X+1  1  1 X+1 X+1  0 X+1 X+1 X+1  X  0  0
 0  0  X  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  X  X  X  X  X  X  X
 0  0  0  X  0  0  0  0  0  0  0  0  0  X  X  0  0  X  0  X  0  0  0  X  X  X
 0  0  0  0  X  0  0  0  0  0  0  0  0  0  0  X  X  X  X  0  X  X  X  0  0  0
 0  0  0  0  0  X  0  0  0  0  0  0  X  X  X  X  0  X  X  0  0  0  X  0  0  0
 0  0  0  0  0  0  X  0  0  0  0  0  X  0  X  X  X  X  0  X  0  X  X  X  0  0
 0  0  0  0  0  0  0  X  0  0  0  X  0  0  X  X  0  0  X  X  0  X  0  X  0  0
 0  0  0  0  0  0  0  0  X  0  0  X  X  X  0  0  0  0  X  0  X  X  X  0  0  0
 0  0  0  0  0  0  0  0  0  X  0  X  X  0  0  X  0  X  0  X  X  0  0  X  X  X
 0  0  0  0  0  0  0  0  0  0  X  X  X  X  X  0  X  0  0  X  X  X  0  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+188x^16+834x^20+3046x^24+3118x^28+843x^32+142x^36+18x^40+2x^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 1.84 seconds.