The generator matrix

 1  0  0  0  0  0  1  1  1  X  1  1  X  1  1  0  0  0  0  1  1  X  1  1  1  1
 0  1  0  0  0  0  0  0  0  1  1 X+1  X  0  1  1  X  1  1  0  X  0  1  0  X X+1
 0  0  1  0  0  0  0  0  0  0  0  0  0  1 X+1  X  X  1 X+1  1  1  X X+1  X X+1  1
 0  0  0  1  0  0  0  1  1  1 X+1  X  1  X  0  X  1  1  0 X+1  0  X  X X+1  1  1
 0  0  0  0  1  0  1  1  X X+1  X X+1  1 X+1  0 X+1  0 X+1 X+1  X  X  1 X+1 X+1 X+1  0
 0  0  0  0  0  1  1  X X+1 X+1  0 X+1  0  0 X+1 X+1  1  X  X  1  0 X+1 X+1  1  0  X
 0  0  0  0  0  0  X  0  X  0  0  0  X  X  X  X  0  0  X  0  X  0  0  X  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+174x^18+548x^20+1001x^22+1484x^24+1661x^26+1688x^28+990x^30+467x^32+132x^34+36x^36+9x^38+1x^42

The gray image is a linear code over GF(2) with n=52, k=13 and d=18.
This code was found by Heurico 1.16 in 30.7 seconds.