In a browser, you will need to use "< pre >" tag to display ascii art, or else the browser will remove spaces and such destroying the formating.
And the extended ASCII is DOS-only, by the way, so it's not a wonder ModPlug will not support it. Besides, why would you, except for the nice shades? You could use Unicode to get the same result. Although you would probably end up needing to click a lot in a character map.
Lines can be drawn using most ordinary ASCII characters like, + - = _ | ! / \ X V < > ( ) U I L H and so on. And shades can be replaced with # $ & %. I do this all the time in my DOS programs.