The generator matrix

 1  0  0  1  1  1  X X^2+X  1  1  1  X  0  1  1 X^2 X^2+X  1  1  1  X  1 X^2  1  1  1
 0  1  0  0  1  1  1 X^2+X X^2+X  X X^2+1  1  1 X+1 X+1  0  1  1 X+1 X^2+X X^2 X^2+X+1 X^2 X^2 X^2+X X^2+1
 0  0  1  1  0 X^2+1  1  1  0  1 X^2+X X^2+X+1 X^2 X+1  1  1 X^2 X^2+X X+1 X^2+X+1  1 X^2+X  1  1  X  1
 0  0  0  X X^2  X X^2+X  X X^2+X X^2  X  0 X^2+X  0 X^2+X X^2+X X^2+X X^2+X X^2+X  X  X  X X^2  0 X^2+X 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+136x^22+180x^23+376x^24+212x^25+332x^26+220x^27+268x^28+124x^29+116x^30+32x^31+43x^32+8x^34

The gray image is a linear code over GF(2) with n=104, k=11 and d=44.
This code was found by Heurico 1.11 in 0.031 seconds.