https://gist.github.com/drhelius/6063288
You can see the comment of the last line is $00fe and the first line is $0000, so assuming the last instruction takes 2 bytes, that's 256 bytes.
Besides, it is a 16 bit machine, so it has 64K addressable space. Going above that requires bank switching. Here is the memory map:
https://gbdev.io/pandocs/Memory_Map.html
I see 32K cartridge ROM (at most), 8K work RAM (built in), 8K video RAM, and some memory mapped devices. At E000, almost 8K is actually wasted as an echo of another range.
As a kid, I once wrote a flame simulation in DOS. The resulting com file was about 100 bytes, so it was possible to write usable programs in <256 bytes. Presumably a very simple DOS text mode game might fit in 256 bytes
See e.g. https://gbdev.io/pandocs/MBC5.html which gives you 8MB as peak ROM size, but it is all paged via the 2nd half of the cartridges address space, in blocks of 16K. Code used by the whole program preferably resides in the first (unbanked) 16K.
This pushes program designs to prefer to either use banking mainly for data (maps/graphics/...), or split the program in independent 16K sized sub-programs that don't communicate too much. If code in bank A uses data from bank B, you'll have to switch back and forth a lot, mediated by unbanked code. You can go all the way, of course, but it is an annoying way to program.
If memory serves, it also checksums the Gameboy logo-intro at the start of every game cartridge -- subjecting non-licensed game publishers to additional copyright claims.
That is quite clever! Don't run without a valid logo, and therefore violate a trademark or copyright if your game is to run without permission. It's like DRM but enforced legally not technically.
"Loaded 128x x 16 h => 2048 bits (256 words)"
If I remember my GB history right this was a DRM measure to stop companies from copying the rest of the game rom and it still work on the actual hardware. Most emulators did not really need it as they had basically figured out what that area was doing anyway. Think in the GBA they even had an animation in there (which you can tweak going by setting a few HW registers) and the ROMS checked to see if the screen memory was correct at startup.