The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  X  1  X  X  X  1  1  X  X  X  X  1  1  X  1
 0  X  0  0  0  X X^2+X  X  0 X^2 X^2  X X^2+X X^2  0 X^2+X  X  X  0  X X^2 X^2+X  0 X^2+X X^2  0
 0  0  X  0  X  X X^2+X  0  0  0  X X^2+X X^2+X  X  X X^2 X^2+X  0 X^2+X  X X^2+X X^2  X  0  0  0
 0  0  0  X  X  0 X^2+X  X X^2  X X^2 X^2 X^2+X  0  X X^2 X^2  X  0 X^2  X  0 X^2  0  X  0
 0  0  0  0 X^2  0  0  0 X^2 X^2 X^2  0 X^2 X^2  0 X^2  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0
 0  0  0  0  0 X^2  0  0  0 X^2  0  0  0  0  0 X^2 X^2 X^2 X^2  0 X^2 X^2 X^2 X^2  0 X^2
 0  0  0  0  0  0 X^2  0 X^2  0  0 X^2  0 X^2  0  0 X^2 X^2  0 X^2  0 X^2 X^2  0  0 X^2
 0  0  0  0  0  0  0 X^2  0  0 X^2 X^2 X^2 X^2 X^2  0  0 X^2  0 X^2 X^2  0 X^2 X^2 X^2  0

generates a code of length 26 over Z2[X]/(X^3) who´s minimum homogenous weight is 18.

Homogenous weight enumerator: w(x)=1x^0+43x^18+70x^19+182x^20+268x^21+389x^22+644x^23+684x^24+1052x^25+1451x^26+1072x^27+785x^28+676x^29+370x^30+252x^31+123x^32+52x^33+49x^34+10x^35+16x^36+1x^38+1x^42+1x^44

The gray image is a linear code over GF(2) with n=104, k=13 and d=36.
This code was found by Heurico 1.16 in 1.24 seconds.