Setting muteHttpExceptions to true in the HTTP request to suppress errors.

gas-muteHttpExceptions.js

/**
 * 備忘録
 * @link https://stackoverflow.com/questions/31891694/handle-404-errors-in-urlfetchapp-fetch
 */

function fetchPage() {
  var response = UrlFetchApp.fetch("http://ctrlq.org/404", {muteHttpExceptions: true});
  if (response.getResponseCode() == 404) {
    Logger.log("Web page not found");
  }
}