"having them carry a letter that said." One or more of the apostles and elders wrote the letter and gave it to Judas and Silas so Judas and Silas could give it to the Gentile brothers.
This is the introduction of the letter. Your language may have a way of introducing the author of the letter and to whom it is written. Alternate translation: "This letter is from your brothers, the apostles and elders. We are writing to you Gentile believers in Antioch, Syria, and Cilicia. Greetings to you" or "To our Gentile brothers in Antioch, Syria, and Cilicia. Greetings from the apostles and elders, your brothers"
Here the word "brothers" refers to fellow believers. By using these words, the apostles and elders assure the Gentile believers that they accept them as fellow believers.