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I'm going to buck the trend here and suggest a really physical storage medium: Print your data out. Or laser engrave it onto sheets of metal or polymer, or whatever you want to do. If you just print pokey old black and white ones and zeros as square pixels on a sheet of 8.5x11" paper at a humble 72 DPI you can store a shade under 47 kilobytes per page without having to resort to any additional trickery. Maybe a kB or two less if you need to leave margins. How much data are you really trying to store?
In a sealed container in the dark you could easily make paper last hundreds of years (we have perfectly intact books sitting on ordinary shelves from the 1800s already), and if you wanted to print on Tyvek or something it'd probably endure thousands.
Reading this back would not be a plug-and-play solution but would have the added advantage of being a purely optical process rather than having to interface with antique storage device electronics on whatever computer you may be using 30 years from now. All you'd need is sheet feed scanner or in a pinch any sufficiently high resolution camera, and the ability to run some kind of programming environment to run a script to read those pixels back into file data.
Maybe this wouldn't be great for archiving your collection of 4k ultra-definition porn, but it'd be absolutely sufficient for storing text and executable data for small programs, plans and schematics, other knowledgy sciency data, and even images... with the added benefit of, if any gestapo thug happens to find this early and dig it up he won't be able to ascertain what that image is just by looking at the piece of paper.
If you actually want to use paper... QR codes. The format is simple, broadly distributed, and has error correction built in. It'll make the whole process a lot easier than trying to roll something yourself.
Another poster here suggested the High Capacity Color Barcode as well, which ought to already have some implementations available somewhere and sports an even higher data density if you're willing (or able) to deal with color.
QR codes are limited to being square in aspect ratio (other than the not terribly helpful "micro rectangular QR" format) and have a maximum payload of ~3kB each. This may not be a great fit for plain consumer paper with a rectangular aspect, and you'd need to jigger some manner of batch reader so's you don't drive yourself insane recovering the data. Neither is an insurmountable problem; I'm just thinking out loud, here.
I’d be wary of one or more colors fading over time unless you are VERY careful with how you print these. Being monochromatic, QR codes don’t have such issues. It would likely also be easier to recover a faded QR code than a colored bar code.
I once heard that some printers print (almost) invisible yellow dots on pages, containing data which helps authority track down whoever printed the page. That might be a risk if the data is really sensitive.
This is true.