It's either that the transaction can be a max of 20 inputs, or the size of the transaction cannot exceed more than 384k bytes. The size of the transaction was the issue, not the number of inputs.
How is your transaction with 15 inputs over 384,000 bytes? Do you only have 1 output? What kind of crazy spending requirements are you using that takes up so much space?
Is there no way around this?
I mean, you probably want to first figure out why you are making such a huge transaction, since you are going to get hit for enormous amounts of fees trying to broadcast that.
Do you have the seed phrase from your ColdCard wallet? If not, you can extract it following the instructions here:
https://coldcard.com/docs/advanced#danger-zone. Import your seed phrase in to Electrum directly and then you can make any transaction you want. Note that if you don't do this on an airgapped computer, then you risk the security of your wallet and all the coins within it.