The generator matrix

 1  0  0  1  1  1 X^2+X  1  1  X X^2  1  0  1  1 X^2+X  1  0  1  1  X  X X^2  1  1  1
 0  1  0  1  0  1  1  X  X  1  1 X+1  0 X+1 X^2+1  1  X  X X^2 X^2  1  1  1 X^2+X X+1  0
 0  0  1  1  1  0  1 X+1  X X^2+X X^2+X+1  X  1 X+1  X  1 X^2+X  1 X+1  1  1  X X^2+X+1 X^2  0  0
 0  0  0  X  0  0  0  0  0  0  0 X^2  X  X X^2+X  X X^2+X X^2 X^2+X  X X^2  X X^2+X  X X^2+X  0
 0  0  0  0  X  0  0  0  X  X  X X^2+X X^2 X^2  0  X  X  X X^2  0 X^2+X  0 X^2+X  0 X^2  0
 0  0  0  0  0  X X^2+X X^2+X  X X^2+X X^2  0  X X^2+X X^2  X X^2 X^2  X X^2  X X^2 X^2 X^2+X  X  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+72x^18+146x^19+427x^20+824x^21+1587x^22+2418x^23+3583x^24+4844x^25+4976x^26+4648x^27+3755x^28+2608x^29+1500x^30+772x^31+376x^32+108x^33+84x^34+14x^35+18x^36+5x^38+2x^39

The gray image is a linear code over GF(2) with n=104, k=15 and d=36.
This code was found by Heurico 1.16 in 11.1 seconds.