The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1 X^2  0  1  1  1  X  1  0  X  1
 0  X  0  0  0  X X^2+X  X  0 X^2  X X^2+X  0 X^2 X^2  X  0  0 X^2 X^2+X X^2+X  X  0 X^2  X X^2+X
 0  0  X  0  X  X  X X^2  0 X^2 X^2+X X^2+X  X  X X^2+X X^2  X X^2  0  X X^2+X  0  0 X^2  0  0
 0  0  0  X  X X^2 X^2+X X^2+X  0 X^2+X X^2 X^2+X  X  0  X  0 X^2+X  X X^2+X  0 X^2  X X^2+X  X X^2+X X^2+X
 0  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2  0  0  0 X^2  0  0 X^2  0 X^2 X^2  0 X^2  0  0  0 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+128x^22+64x^23+81x^24+192x^25+144x^26+192x^27+24x^28+64x^29+96x^30+21x^32+16x^34+1x^40

The gray image is a linear code over GF(2) with n=104, k=10 and d=44.
This code was found by Heurico 1.16 in 3.86 seconds.