Calling a google apps script execution api from PHP using a service account

I'm trying to call a very simple google apps script from php using a service account so that only my server can access it, not users of the website.

Here is how I do. I create the script here https://script.google.com

function get() {
    return  ContentService.createTextOutput('get method');
}

and a new project is automatically associated when i save it. Then I open File > Project Properties to get the scriptId = MM8zQqofS1OIcnFiNSlm1CGEl5qMrMVBt

I access the developer console of the associated project threw Resources > Project Developers console by clicking on the project link at the top of the popup displayed.

Then I click 'Activate and manage API' and activate the 'Google Apps Script Execution API'. I click on 'Credentials' and see that the previous operation automatically created OAuth2 credentials. But what I need is service account credentials. Then I create one Add credentials > Service account and download generated p12 file. I get the clientId = 109160023321840004240 and clientMail = [email protected] for this service account.

I go back to my script and share it with the service account email with read&write access File > Share. First of all i get an email in my personal mailbox which notifies me that

Delivery to the following recipient failed permanently:

 [email protected]

Then I publish the script as an execution API Publish > Publish as an execution API with access to everybody.

Now lets go on the PHP server side. Using the 'Google APIs Client Library for PHP' available here https://github.com/google/google-api-php-client I try to call my script function from PHP:

$client = new Google_Client();
$client->setClientId('109160023321840004240');
$client->setApplicationName('myScript');

$cred = new Google_Auth_AssertionCredentials(
    '[email protected]',
    [/*no scope nedeed for this simple script*/],
    file_get_contents('path_to_myScript.p12')
);
$client->setAssertionCredentials($cred);

if ($client->getAuth()->isAccessTokenExpired()) {
    $client->getAuth()->refreshTokenWithAssertion($cred);
}

$service = new Google_Service_Script($client);
$scriptId = 'MM8zQqofS1OIcnFiNSlm1CGEl5qMrMVBt';

// Create an execution request object.
$request = new Google_Service_Script_ExecutionRequest();
$request->setFunction('get');
$response = $service->scripts->run($scriptId, $request);

And here is the response I get all the time

Error calling POST https://script.googleapis.com/v1/scripts/MM8zQqofS1OIcnFiNSlm1CGEl5qMrMVBt:run: (403) The caller does not have permission

If, when I deploy the script, I choose to give access to 'Me only', i get the following response.

Error calling POST https://script.googleapis.com/v1/scripts/MM8zQqofS1OIcnFiNSlm1CGEl5qMrMVBt:run: (404) Requested entity was not found.

I would be so happy if one of you have an idea to help me :)