The generator matrix

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

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+72x^16+38x^18+321x^20+362x^22+864x^24+732x^26+927x^28+372x^30+307x^32+30x^34+63x^36+2x^38+4x^40+1x^44

The gray image is a linear code over GF(2) with n=52, k=12 and d=16.
This code was found by Heurico 1.16 in 0.528 seconds.