I don't suppose anybody knows how the point system works at the end of the game? It is similar to Civ, Colonization and Pirates!. But do you get more points for having a child heir or an adult heir? How much does your general and swordfighting contribute? How much does each difficulty level add? Etc.
hector13 nailed it, but I wanted add a little.
The difficulty you play on modifies the score. On Wakizashi mode, 3000 points, or a 100 year dynasty, is pretty much the maximum. You have to move on to Katana or higher to be eligible for a 200 year dynasty. I'm not sure what the max dynasty is on No-dachi mode, because playing that difficulty makes me want to bash my head into a wall.
Swordfighting counts for nothing, as far as I can tell.
Max army size is just over 12k (something like 12800?).
Not sure if child or adult heir makes a difference.
I think hector13 is right about "unsurpassed" being the highest honor. Your honor bar might be maxed out, but don't quit until you see that word.
Getting max generalship is tricky, since you can't train the last couple points. You have to battle. If you're quite strong, most people will not want to fight you. That's why I encourage at least one rival to have a big army.