Yeah sadly as the post above me said the game officially runs in CGA so if you want apply a EGA patch I would recommend the ultima patcher,
http://www.ultimaaiera.com/ultima1/pixs-ultima-patcher/ , which can apply fixes to any Ultima game and you don't have to worry about playing around with Dosbox to apply the fixes and upgrades, well outside of the newest Exodus graphic and music patch which adds VGA and composite CGA graphics on top of EGA and default 4 colour CGA since the patcher program doesn't have that one, just the old midi and EGA patch.
Now I would also like to point out both it(Ultima 2 and Exodus) were intended to make use of the colour "smudging" of composite video monitors to turn the 4 basic colours of the CGA colour pallet into 16 sadly while Dosbox does have a feature that allows most CGA games to have their intended Composite CGA colour pallet, Ultima 2 and 3 are not supported.
But you can see what Ultima 2 is supposed to look like here if your intrested