The generator matrix

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

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+85x^18+266x^20+483x^22+765x^24+902x^26+757x^28+506x^30+241x^32+69x^34+16x^36+3x^38+1x^40+1x^44

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 25.7 seconds.