The generator matrix

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

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+77x^20+172x^21+474x^22+660x^23+956x^24+1168x^25+1134x^26+1304x^27+942x^28+636x^29+358x^30+148x^31+131x^32+8x^33+18x^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 0.921 seconds.