If you just need a quick answer (to decide if something else is going to work how you need), then you can do this with Wolfram|Alpha. Go there:
http://www.wolframalpha.com/
and input "factor x^26-1" and press the "equal" button. It'll show some info about the polynomial, including the factors mod 2. In many boxes, there's a link for "Show More". Press the one attached to the factors over GF(2), and it'll show you the factors over GF(3). In this case, you get
$$(x+1) (x+2) (x^3+2 x+1) (x^3+2 x+2) (x^3+x^2+2) (x^3+x^2+x+2) (x^3+x^2+2 x+1) (x^3+2 x^2+1) (x^3+2 x^2+x+1) (x^3+2 x^2+2 x+2).$$
Annoying to have "2" instead of "-1" in GF(3), but that's the price of having a machine do your work for you.
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