Tratando de encontrar cómo publicar en Google Plus Wall desde PHP, pero obtuve 403 incluso usando el explorador de APIa consiguió el

{
 "error": {
  "errors": [
   {
    "domain": "global",
    "reason": "forbidden",
    "message": "Forbidden"
   }
  ],
  "code": 403,
  "message": "Forbidden"
 }
}

Mi código PHP se ve así:

    $client = new \Google_Client();
    $client->setApplicationName("Speerit");
    $client->setClientId($appId);
    $client->setClientSecret($appSecret);
    $client->setAccessType("offline");        // offline access
    $client->setIncludeGrantedScopes(true);   // incremental auth
    $client->setAccessToken(
        json_encode(
            array(
                'access_token' => $accessToken,
                'expires_in' => 3600,
                'token_type' => 'Bearer',
            )
        )
    );
    $client->setScopes(
        array(
            "https://www.googleapis.com/auth/userinfo.email",
            "https://www.googleapis.com/auth/plus.me",
            "https://www.googleapis.com/auth/plus.stream.write",
        )
    );
    $client = $client->authorize();

    // create the URL for this user ID
    $url = sprintf('https://www.googleapis.com/plusDomains/v1/people/me/activities');

    // create your HTTP request object
    $headers = ['content-type' => 'application/json'];
    $body = [
        "object" => [
            "originalContent" => "Happy Monday! #caseofthemondays",
        ],
        "access" => [
            "items" => [
                ["type" => "domain"],
            ],
            "domainRestricted" => true,
        ],
    ];
    $request = new Request('POST', $url, $headers, json_encode($body));

    // make the HTTP request
    $response = $client->send($request);

    // did it work??
    echo $response->getStatusCode().PHP_EOL;
    echo $response->getReasonPhrase().PHP_EOL;
    echo $response->getBody().PHP_EOL;

Siguiendo la documentación oficial y algunas referencias de otras publicaciones