The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  0  X X^2  X  1  X X^2  0 X^2
 0  X  0  0  0  X X^2+X  X  0 X^2 X^2  0  X X^2+X  X X^2+X X^2+X X^2  0 X^2 X^2  0  X  X X^2  X
 0  0  X  0  X  X X^2+X  0  0  0 X^2+X X^2+X  X  X X^2  0  X X^2  X  X X^2+X  0 X^2 X^2+X  X X^2
 0  0  0  X  X  0 X^2+X  X X^2 X^2+X  X X^2 X^2  X  X X^2  0  X  X X^2+X X^2+X X^2 X^2+X X^2 X^2 X^2+X
 0  0  0  0 X^2  0  0  0 X^2  0  0  0  0  0  0 X^2 X^2  0 X^2 X^2 X^2 X^2  0  0 X^2 X^2
 0  0  0  0  0 X^2  0 X^2  0  0 X^2 X^2  0 X^2 X^2  0  0  0  0 X^2 X^2 X^2  0  0 X^2  0
 0  0  0  0  0  0 X^2 X^2 X^2 X^2  0  0 X^2  0  0  0  0 X^2 X^2 X^2  0 X^2  0  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+166x^20+24x^21+344x^22+152x^23+650x^24+336x^25+782x^26+336x^27+634x^28+152x^29+318x^30+24x^31+141x^32+26x^34+8x^36+2x^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 0.399 seconds.