The generator matrix

 1  0  0  1  1  1  X  1  1 X^2  1  1 X^2  X X^2+X  X  1  1  1  1 X^2+X X^2  1 X^2 X^2  1
 0  1  0  1 X^2+X X^2+X+1  1 X^2 X^2+X  X X^2+1 X^2+X+1  1  1  0  X X^2 X+1 X^2+X  X  1 X^2+X X+1  1  1 X+1
 0  0  1  1 X^2+X+1 X^2+X  1  X X^2+1  1 X+1 X^2  X X^2+X+1  1  1 X^2 X+1 X^2  1  0  1 X^2 X^2+X X^2+X+1  0
 0  0  0 X^2  0  0  0  0  0  0 X^2  0 X^2 X^2 X^2 X^2 X^2 X^2  0  0  0 X^2 X^2  0  0  0
 0  0  0  0 X^2  0  0  0 X^2  0 X^2 X^2 X^2 X^2  0 X^2 X^2  0  0 X^2 X^2 X^2  0 X^2 X^2 X^2
 0  0  0  0  0 X^2  0  0  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2 X^2  0 X^2
 0  0  0  0  0  0 X^2 X^2 X^2 X^2  0  0  0 X^2 X^2  0  0  0  0 X^2 X^2 X^2 X^2  0  0  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+100x^20+156x^21+530x^22+456x^23+1152x^24+948x^25+1550x^26+848x^27+1240x^28+548x^29+398x^30+104x^31+119x^32+12x^33+18x^34+12x^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 0.897 seconds.