How can the code provided be improved to enhance security and prevent spam submissions?

The issue with the current code is that it does not have any form of validation or protection against spam submissions. To enhance security and prevent spam, we can implement a CAPTCHA system to ensure that the form is being submitted by a human user.

```php
<?php
session_start();

// Generate a random CAPTCHA code
$captcha_code = rand(1000, 9999);
$_SESSION['captcha_code'] = $captcha_code;

// Display the CAPTCHA image on the form
echo '<img src="captcha_image.php" alt="CAPTCHA image">';

// Validate the CAPTCHA code on form submission
if(isset($_POST['submit'])){
    if($_POST['captcha'] == $_SESSION['captcha_code']){
        // CAPTCHA validation successful, process the form submission
        // Add your form processing logic here
    } else {
        // CAPTCHA validation failed, display an error message
        echo 'Invalid CAPTCHA code, please try again.';
    }
}
?>
```

In the above code snippet, we generate a random CAPTCHA code and store it in a session variable. We then display the CAPTCHA image on the form for the user to input. Upon form submission, we validate the entered CAPTCHA code against the one stored in the session. If the codes match, the form submission is processed; otherwise, an error message is displayed. This helps prevent automated spam submissions by ensuring that a human user is interacting with the form.