His lawyer, Tom Sutcliffe, said Barnett was in the process of trying to get the bodies of his wife, Tamara, and friends Ruth and Mitchell Peterson back home to Utah.
Judge David Ruth adjourned the case to assess if a restorative justice conference between the truck driver and Barnett could be dismissed, given the driver had indicated no desire to take part.
The trio were killed on the outskirts of Hamilton on Wednesday night when Barnett turned right at the intersection of State Highway 39 and Tuhikaramea Rd, into the path of a southbound truck.
Barnett, an orthodontist, was driving and suffered moderate injuries.
It is expected Barnett will be sentenced today so he can return to the United States to bury his wife and friends.
Mr Sutcliffe said Barnett's eldest son Christopher was en route from the US to help his father return home.
He was expected to arrive later this afternoon.
He said Barnett was too upset to speak publicly but wanted to express his gratitude for the kindness and support received from the local community and praised police and emergency services as professional and compassionate.
Mr Sutcliffe said the crash had devastated two families and the close knit community of Richfield, where the couples were "pillars of strength characterised by their selfless service over many years".
The case is expected to continue at 3pm.
The couples, both from Utah, were members of Church of Jesus Christ of Latter-Day Saints and were on their way to the Mormon temple on the outskirts of Hamilton when the crash happened at 5.30pm on Wednesday.
It appeared that Barnett turned to drive on to the side road off the state highway where the temple is located, right into the path of an oncoming truck and trailer unit.
Police announced this afternoon that the 56-year-old had been charged with three counts of careless driving causing death.
"Wednesday's tragedy is being investigated by a number of teams and from the police's perspective we are acting on behalf of the Coroner," said Detective Sergeant Dave Grace.
"The crash investigation is still in its formative stages and it is too early to comment on the cause of the crash. As we mentioned yesterday police would like to express our condolences to the families for their loss."