The generator matrix

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

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+168x^23+370x^24+260x^25+336x^26+164x^27+274x^28+140x^29+116x^30+36x^31+41x^32+4x^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 0.058 seconds.