The code you have posted seems to be a mish mash of the code from the modules synopsis, and different parts of the documentation.

my $code = "I didn't find in documentation, what is this code, and how
+ do I get it";
$instagram->code($code);
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Both the instagram docs and the example code for the new constructor show how to specify the response type, which I suggest you try:

use API::Instagram;
 
my $instagram = API::Instagram->new({
                client_id     => 'xxxxxxxxxx',
                client_secret => 'xxxxxxxxxx',
                redirect_uri  => 'http://localhost',
                scope         => 'basic',
                response_type => 'code'
                granty_type   => 'authorization_code',
});
 
print $instagram->get_auth_url;
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In fact the lines following your attempt match those that follow this type of usage.

I already got this part, i.e.: logged in and got auth url. What's next?
As I said, I can't figure out how to authenticate and ultimately, list posts.
I would really appreciate a working code example.
Thank You.