The generator matrix

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

generates a code of length 26 over Z2[X]/(X^3) who´s minimum homogenous weight is 22.

Homogenous weight enumerator: w(x)=1x^0+310x^22+422x^24+618x^26+430x^28+202x^30+41x^32+22x^34+2x^36

The gray image is a linear code over GF(2) with n=104, k=11 and d=44.
This code was found by Heurico 1.16 in 16.9 seconds.