The generator matrix

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

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+187x^18+550x^20+24x^21+1111x^22+440x^23+2429x^24+1584x^25+3652x^26+1584x^27+2510x^28+440x^29+1196x^30+24x^31+495x^32+121x^34+28x^36+5x^38+3x^40

The gray image is a linear code over GF(2) with n=104, k=14 and d=36.
This code was found by Heurico 1.16 in 5.28 seconds.