There are ways to keep more chunks loaded but if you are on a server they might not be available to you of may be frowned upon or forbidden as causing more lag.
Depending on how long the minecart line is and how powerful the computer raising the render distance could be enough.
Or moving the world spawn so that the far end of the minecart line is in the spawn chunks.
Another way, unless things have changed since I read about them, is chunk loaders.
Basically, starting at the spawn chunks or somewhere close enough to you that it would be loaded, like 1/3 of the way along the minecart line, you have pairs of hoppers or dispensers or something at every chunk border passing items back and forth which forces the game to load the next chunk.
Also it seems that in 1.13.1 a set of commands were added (/forceload) that let you set up a list of chunks that are always kept loaded.
(The Wiki hints that something about that changed in 1.13.2 but I can't find any info on what may have changed.)