The generator matrix

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

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+510x^22+980x^24+1214x^26+864x^28+442x^30+75x^32+10x^34

The gray image is a linear code over GF(2) with n=104, k=12 and d=44.
This code was found by Heurico 1.11 in 121 seconds.