Error with SMTP host in PHPMailer - php

Question

I'm trying to send an email and the PHPMailer is returning the following message:
SERVER -> CLIENT:
CLIENT -> SERVER: EHLO my-domain.com
SERVER -> CLIENT:
SMTP ERROR: EHLO command failed:
SMTP NOTICE: EOF caught while checking if connected
SMTP connect() failed.
Mailer Error: SMTP connect() failed.
My domain is my-domain.com
Here is my page that sends the email:
<?php
//SMTP needs accurate times, and the PHP time zone MUST be set
//This should be done in your php.ini, but this is how to do it if you don't have access to that
date_default_timezone_set('Etc/UTC');
require '../PHPMailerAutoload.php';
//Create a new PHPMailer instance
$mail = new PHPMailer();
//Tell PHPMailer to use SMTP
$mail->isSMTP();
//Enable SMTP debugging
// 0 = off (for production use)
// 1 = client messages
// 2 = client and server messages
$mail->SMTPDebug = 2;
//Ask for HTML-friendly debug output
$mail->Debugoutput = 'html';
//Set the hostname of the mail server
$mail->Host = "smtp.gmail.com";
//Set the SMTP port number - likely to be 25, 465 or 587
$mail->Port = 465;
//Whether to use SMTP authentication
$mail->SMTPAuth = true;
$mail->SMTPSecure = "tls";
//Username to use for SMTP authentication
$mail->Username = "sender#domain.com";
//Password to use for SMTP authentication
$mail->Password = "myPassword";
//Set who the message is to be sent from
$mail->setFrom('webmaster#example.com', 'First Last');
//Set an alternative reply-to address
$mail->addReplyTo('webmaster#example.com', 'First Last');
//Set who the message is to be sent to
$mail->addAddress('me#domain.com', 'John Doe');
//Set the subject line
$mail->Subject = 'PHPMailer SMTP test';
//Read an HTML message body from an external file, convert referenced images to embedded,
//convert HTML into a basic plain-text alternative body
$mail->msgHTML(file_get_contents('contents.html'), dirname(__FILE__));
//Replace the plain text body with one created manually
$mail->AltBody = 'This is a plain-text message body';
//Attach an image file
$mail->addAttachment('images/phpmailer_mini.png');
//send the message, check for errors
if (!$mail->send()) {
echo "Mailer Error: " . $mail->ErrorInfo;
} else {
echo "Message sent!";
}
?>
As you can see, my smtp host is set to smtp.gmail.com and it seems tha PHPMailer is trying to send the email via another host, in the case, the same as where my app is hosted (my-domain.com).
Why is it happening?