Thanks to /u/ssokolow and /u/mmstick for a solution!
I did:
sudo apt install mingw-w64
I had to create ~/.cargo/config/ and write:
[target.x86_64-pc-windows-gnu]
linker = "x86_64-w64-mingw32-gcc"
ar = "x86_64-w64-mingw32-gcc-ar"
Then I just did:
cargo build --release --target=x86_64-pc-windows-gnu --verbose
Thanks again, everyone, for all of your help!