A race of people was created through magic, their mind was greatly altered, among the abilities that were granted was a memory that perfectly records all sensory information forever. As well as the ability to run programs in a sort of secondary mechanical mind, that operates on a much faster magical substrate.
This allows them to do things like instantly look at something like a QR code and know what's encoded (provided they have the mental program that reads QR codes).
Setting is roughly your standard D&D esque fantasy (with this group's abilities making them nearly the only people capable of being general mages) but with some basic mechanical innovation like typewritters and the printing press. The world runs on magic, which makes most technology impossible, chemistry just doesn't work and the world resembles the ways people thought the world worked pre enlightenment.
For these people there is no reason not to have a language as complex as possible when communicating with others sharing their abilities. They will all share the same same language since they can learn it in hours or days and tend to greatly value efficiency.
So with that in mind what would you would expect from their language:
I'm looking for the rough analogs for their spoken and written languages. The only limit to the sounds they can distinguish are the physical features of their ears, so you could pack in some massive bandwidth here. It's also important to note that their mental programs can produce sounds automatically, so no sound is more unpleasant to produce than any other, the only limits are what sounds they can physically produce. I also think they'd want to put in some physical motions here, this wouldn't just have to be stuff like sign language they could assign meaning to slight twitches in facial muscles or blinks.
As for their analog of written language, it's important to mention that this race almost universally has slight hand tremors, so that would make drawing fine detail quite hard (so hand drawn QR codes are right out). The only fundamental limit to how quickly they can read is how quickly they can move their eyes. This language doesn't have to be done with a pen, what I'm looking for here is something they can put on paper or something similar quickly. If your solution involves a very simple cheap machine or say the use of a knife to get straight lines that's fine. You might also have another type of writting that would be used for books, where the difficulty of transcribing by hand wouldn't be a factor.
Reminder: There's no reason to have this language resemble any language ever previously devised, in fact it seems really unlikely it would. Given how easy learning a language is for these people, there's no reason they wouldn't adopt whatever written and spoken systems were invented by linguists to maximize information bandwidth.
Given the much higher bandwidth of this language it really ought to be basically indecipherable to vanilla humans, if they can understand it after all then it must be relatively simple, which there's no reason this language would be.