The generator matrix

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

generates a code of length 26 over Z2[X]/(X^2) who´s minimum homogenous weight is 18.

Homogenous weight enumerator: w(x)=1x^0+41x^18+78x^19+150x^20+206x^21+268x^22+314x^23+343x^24+422x^25+416x^26+430x^27+402x^28+330x^29+251x^30+190x^31+119x^32+66x^33+47x^34+12x^35+8x^36+1x^40+1x^46

The gray image is a linear code over GF(2) with n=52, k=12 and d=18.
This code was found by Heurico 1.16 in 0.548 seconds.