All of Arnold Rimmer's brothers were known to have been assigned to Quantum Twister class starships. Howard was a vending machine repair operative aboard the Columbus 3, but had lied to his family to convince them he was a captain. He evidently died at some point in the ship's mission and was resurrected as a hologram, possibly to keep a particular crewmate sane. The crew seemed to consist of humanoids recruited from different species and mechanoids.
Millions of years into deep space the Columbus 3 was seemingly attacked by a hostile force and Howard was one of two survivors, Sim Crawford being the other. They sent out a distress call to any Space Corps vessel and, due to the coincidental nature of the Quantum rod, he managed to get through to his brother Arnold aboard the SS Trojan. Despite being capable of teleporting them instantly to the Trojan, Arnold insisted that they would have to fly to him, giving him 15 hours to become an officer and impress his brother.
After failing his revision again, Arnold hit upon another idea - cheating. He dressed in a captain's uniform and convinced his shipmates to play along as his senior staff. When Howard and Crawford beamed aboard, they were impressed by the lavish technology of the Trojan, not realising that it was being towed along by Red Dwarf.
Eventually Howard admitted that he was just a technician and that he had hidden during the attack that had killed his crew. Crawford then came clean, confessing that it was she who had killed them and then started shooting, killing Howard Rimmer in the crossfire. Her hopes of leading a simulant revolution were dashed when The Cat overloaded her neural net with a resentment file.
Behind the scenes
Although the Columbus 3 was never seen on-screen, it can be reasonably assumed that it was similar to the Trojan. However, since Howard and Crawford were impressed by the technology of the Trojan and asked for a tour, the Columbus 3 was perhaps an older model or variant.