4000^4 gives 256000000000000 giving 3.3 bits of entropy per decimal digit it comes to 50 bits of entropy. Not too shabby but not that secure either. Your PCs rng may play you dirty tricks.
And of course there are all kind of legacy systems with password limitations to 32 or 16 character, but above 8 etc etc which would further reduce the pool.
Of course you could try your own password deriving mechanism. Take the first 16 characters of bcrypt(username,site domain) it will produce awesome passwords for any site that you will have easy time producing when needed. Until the hackers begin to suspect what you use if it becomes widespread.
(Disclaimer - not a cryptographer or security expert or particularly competent in anything)