Hello world
I am totally overthinking this but…
Spoiler-ish
… with six trits giving you integers between 0 and 728 you could add, say, ‘010111’ (=256, or ’ B BBB’) as the first line, definitely not in ASCII Kansas any more, and ‘000000’ as the last (NUL being the traditional end of string marker, alternatively choose the end of string marker of your choice), giving our first instruction in this language as ‘PRINT’, being represented by ‘010111’ in base three, which will print everything thereafter until the next NUL as an ASCII string. How you want to handle attempts to print values > 255 at that point is of course up to you. Perhaps it could support the first 728 characters of UNICODE 
Honestly, I was expecting the first and last characters to be some random - by which I mean unprintable - stuff of this sort, with the characters in between being recognisable ASCII.
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This is why I love nerds 