Well, I'm not much of a min-maxer, so I'm sure someone else could step in here with a better build, but just off the top of my head I would go with an Ork for the wee bit of extra body, thereby upping our armor "cap" so we don't get penalties. 7 body wouldn't be unheard of if you're building a super-shooty tank type toon I would think. Trolls get +1/+1 armor base and have a higher base Body stat, but I'm trying to show that most characters can get there, not that trolls are OP or some other randomness.
Now lets see (gotta break the books out - never actually tried to make a crazy armor beast)...
Form fitting body armor = 6/2
PPP = +2/+4 (+2/+6 w/ helmet)
Armored Jacket or Camo Suit = 8/6
Subtotal for only worn armor = 16/12 (16/14 w/ helmet) [only counts as 13/11 (13/13 w/ helmet) for encumbrance] *
To this subtotal we can add either trolls natural armor, some sort of dermal plating, dermal sheath, orthoskin, bone lacing or mystic armor, etc., bringing our total even higher - still with no penalties, and if you did somehow incur a penalty, it would not be out-of-line to pump your body up by one more - using either BP/karma to up your natural, or by addding cyber/bioware to the mix. Also note that:
* If your GM interprets the rules for FFBA + PPP as "Add the PPP to the FFBA, then divide its armor by 2 for encumbrance", then this combo can be worn with a Body 6, rather than requiring a Body of 7 due to the armor set only counting as 12/9 (12/10 w/ helmet) for encumbrance in that case. I do not run it like this, but I have heard of others interpreting the rules that way.
So anyway, even an elf could get really close to this setup no problem, especially when you add in the mystic armor or bio/cyberware. But as I said before, I don't really have much of an issue with the min-maxing or what have you, I don't care if people build tanks, what bothers me is all the tons of extra dice rolling required which tends to slow down combat.