As I can’t seem to find all the Braintree error codes in a nice, formatted list, I’ve parsed this page and put the results in various formats, available here (CSV, JSON, PHP Array)
You can also find these in the PHP SDK, in \Braintree\Error\Codes.php class as constants.

You could do something like

$braintreeCodes = new ReflectionClass('Braintree_Error_Codes');

in order to have them into an array, but you won’t have a description/explanation for each code.

Using the PHP Gist you can also provide your clients with a detailed explanation of why the payment process failed. If you think that’s a good ideea 🙂