The generator matrix

 1  0  0  0  0  1  1  1  0  1  1  1  1  X  0  0  1  1  1  0  1  1  1  1  1  1
 0  1  0  0  0  0  1  0  0  0  X X+1  1  1  1  0  X X+1  1  X X+1  0  0  X X+1  0
 0  0  1  0  0  0  1  1  1 X+1  1 X+1  X X+1 X+1  1  0 X+1 X+1  X  0  0  0  X  X  0
 0  0  0  1  0  1  0  1 X+1  X  0 X+1 X+1  X  X X+1  1  0  1  1 X+1  1  X X+1 X+1  0
 0  0  0  0  1  1  1  X  1  1  0  0  1  0 X+1  0  X  X X+1  1 X+1  0  0 X+1  1  0
 0  0  0  0  0  X  0  0  X  0  X  X  0  X  X  X  X  X  0  0  0  0  X  X  0  0
 0  0  0  0  0  0  X  0  0  0  0  0  0  0  X  X  X  X  X  X  X  X  X  X  X  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+68x^18+56x^19+174x^20+224x^21+275x^22+320x^23+322x^24+412x^25+338x^26+444x^27+380x^28+344x^29+276x^30+184x^31+131x^32+44x^33+66x^34+20x^35+14x^36+1x^38+2x^40

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 0.558 seconds.