Have I just lost all my bitcoin?

Since you haven't practised recovery, that is possible. Likely even.

there is NOWHERE to put the 16 characters code.

It's not obvious what that 16-character code might represent.

• CoPay uses a 12-word recovery phrase (sometimes called a "recovery seed" or "wallet seed")
• Bitcoin private-keys are 256-bit numbers usually shown as 64 hexadecimall characters

You normally need one of those or a wallet backup file .

What you can do

• Contact CoPay / BitPay
• Read the CoPay FAQ
• Read about CoPay recovery
• Ask new questions here about anything specific you need help with.

I'm posting this answer because it could apply to any wallet application or service, but is limited in scope to regaining access to funds only (not restoring full functionality of a specific wallet application. The following requires a lot more technical work than the OP is likely asking, but the point is that it is feasible based on common standards.

According to CoPay Source, it appears to be following BIP39 standard for mnemonics (recovery phrase) and BIP32 standard for hierarchical deterministic wallets, it should be possible to regenerate your keys outside of their application.

Steps to regenerate

1. Generate the seed from the mnemonic (and password if originally used) following the standard method outlined in BIP39 - From Mnemonic to Seed. There are many open source libraries that implement this functionality (including CoPay itself).
2. Generate the key pairs in the hierarchy from the seed using BIP32 Key Derivation Standard also implemented in many projects including CoPay.
3. Convert the generated private keys to the required format for wallet import. Usually this is a WIF format (e.g. for Bitcoin-core wallet).

Some potential problems:

1. The original wallet application didn't implement BIP39 correctly, or made some changes.
2. You aren't able (with reasonable effort) to generate all of the keys because the hierarchical structure CoPay uses was unknown.