The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1 X^2  0  X X^2  0  X  X  X
 0  X  0  0  0  0  0  0  0  X X^2+X  X X^2 X^2  X  0 X^2 X^2+X  X  X  0  X X^2  X X^2 X^2
 0  0  X  0  0  0  X X^2+X  X  X  X  0  0  X X^2  X X^2+X X^2+X X^2  0  0  X  X X^2  X  X
 0  0  0  X  0  X  X  X X^2  0  0 X^2 X^2 X^2 X^2+X X^2+X  0  X X^2+X X^2+X  X X^2 X^2+X  0  0  X
 0  0  0  0  X  X X^2 X^2+X X^2+X  0  X  X  0 X^2+X  X X^2  X X^2+X X^2 X^2+X  X X^2  0 X^2+X  0 X^2+X
 0  0  0  0  0 X^2 X^2 X^2 X^2 X^2  0  0 X^2  0 X^2  0 X^2  0  0 X^2  0 X^2 X^2 X^2  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+174x^20+16x^21+376x^22+132x^23+571x^24+372x^25+822x^26+360x^27+621x^28+120x^29+332x^30+20x^31+132x^32+4x^33+38x^34+5x^36

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 0.337 seconds.