The generator matrix

 1  0  1  1  1 X^2+X  1 X^2  1  1  1 X^2 X^2  0 X^2+X  1 X^2  1  1 X^2  1 X^2+X  1  1  X  1
 0  1  1  0 X^2+X+1  1  X  1 X+1 X^2+X X^2+1  1  1  1  1 X^2  1 X+1 X+1  1  0  1  0  0  0  0
 0  0  X  0 X^2+X  0  0 X^2  X  0 X^2+X X^2  0  X  X  X  X  0 X^2  X X^2+X X^2  X X^2+X  0  0
 0  0  0  X  0  0 X^2+X X^2+X  X X^2  X X^2+X X^2  X X^2  0 X^2  0 X^2  X  X X^2  X  0 X^2  0
 0  0  0  0 X^2  0 X^2  0 X^2  0 X^2 X^2 X^2  0  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0  0  0
 0  0  0  0  0 X^2  0  0 X^2 X^2  0 X^2 X^2 X^2  0  0 X^2 X^2  0  0 X^2 X^2  0  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+79x^20+140x^21+166x^22+298x^23+453x^24+606x^25+657x^26+526x^27+439x^28+386x^29+189x^30+70x^31+46x^32+18x^33+11x^34+2x^35+6x^36+2x^37+1x^38

The gray image is a linear code over GF(2) with n=104, k=12 and d=40.
This code was found by Heurico 1.16 in 0.241 seconds.