The generator matrix

 1  1  1  1  1  1  1  1  1  1  X  0  1  X  0  1  1  1  1  X  0  1  1  1  X  1
 0  X  0 X^2+X  0 X^2+X  0 X^2+X  0 X^2+X X^2+X  X X^2 X^2+X  X  0 X^2+X X^2+X X^2 X^2+X  X  0 X^2+X X^2+X X^2+X  0
 0  0 X^2  0  0  0  0  0  0  0  0  0  0  0 X^2 X^2 X^2 X^2  0 X^2 X^2 X^2  0 X^2  0  0
 0  0  0 X^2  0  0  0  0  0  0 X^2 X^2  0 X^2 X^2  0 X^2  0  0  0  0 X^2 X^2 X^2  0 X^2
 0  0  0  0 X^2  0  0  0  0  0 X^2 X^2 X^2  0  0 X^2  0  0 X^2 X^2  0 X^2 X^2 X^2  0 X^2
 0  0  0  0  0 X^2  0  0  0 X^2  0 X^2  0 X^2  0 X^2 X^2 X^2 X^2 X^2  0  0 X^2 X^2  0 X^2
 0  0  0  0  0  0 X^2  0  0  0  0 X^2 X^2 X^2 X^2 X^2  0 X^2 X^2 X^2 X^2  0  0 X^2 X^2  0
 0  0  0  0  0  0  0 X^2  0 X^2 X^2  0  0 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2  0 X^2  0  0  0
 0  0  0  0  0  0  0  0 X^2  0 X^2  0 X^2 X^2 X^2  0  0 X^2  0 X^2  0  0 X^2 X^2  0  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+37x^18+12x^19+96x^20+68x^21+186x^22+300x^23+421x^24+644x^25+574x^26+644x^27+412x^28+300x^29+200x^30+68x^31+81x^32+12x^33+21x^34+12x^36+6x^38+1x^40

The gray image is a linear code over GF(2) with n=104, k=12 and d=36.
This code was found by Heurico 1.16 in 0.319 seconds.