New Jersey Transit train engineers went on strike Friday, leaving an estimated 350,000 commuters in New Jersey and New York City to seek other means to reach their destinations or consider staying home. Groups of picketers gathered in front of transit headquarters in Newark and at the Hoboken Terminal, carrying signs that said “Locomotive Engineers on Strike” and “NJ Transit: Millions for Penthouse Views Nothing for Train Crews.” Passing drivers honked their horns. The walkout comes after the latest round of negotiations on Thursday didn’t produce an agreement.