The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  1  1  1  1  1  1  1  1  1  1
 0  X  0  0  0  0  0  0  0 X^2+X  X  X  X  X X^2 X^2  X X^2+X  0 X^2+X  X X^2+X X^2  0 X^2+X  0
 0  0  X  0  0  0  X X^2+X  X X^2  X X^2+X  0 X^2  X  0 X^2+X X^2  X  X X^2  X X^2 X^2  X  0
 0  0  0  X  0  X  X  X  0 X^2+X X^2  X X^2+X X^2  X  0  X  X  X X^2+X X^2+X  X X^2  X  X  0
 0  0  0  0  X  X  0  X X^2+X  X  0  X X^2 X^2+X  X  X  X X^2 X^2 X^2 X^2+X X^2+X  0  0  0  0
 0  0  0  0  0 X^2  0  0  0  0  0  0  0 X^2 X^2  0 X^2  0 X^2 X^2 X^2 X^2 X^2  0  0  0
 0  0  0  0  0  0 X^2  0 X^2  0 X^2 X^2 X^2 X^2 X^2 X^2  0  0 X^2 X^2 X^2 X^2 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+72x^18+74x^19+164x^20+206x^21+270x^22+290x^23+338x^24+1470x^25+2404x^26+1478x^27+342x^28+314x^29+274x^30+198x^31+165x^32+58x^33+51x^34+8x^35+14x^36+1x^50

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 1.36 seconds.