The generator matrix

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

generates a code of length 26 over Z2[X]/(X^3) who´s minimum homogenous weight is 20.

Homogenous weight enumerator: w(x)=1x^0+189x^20+72x^21+506x^22+512x^23+1132x^24+880x^25+1502x^26+1120x^27+1102x^28+392x^29+502x^30+96x^31+131x^32+50x^34+5x^36

The gray image is a linear code over GF(2) with n=104, k=13 and d=40.
This code was found by Heurico 1.16 in 1.18 seconds.