Warwicks without Coventrian Ian Bell, who is expected to bat at number four for England in the Edgbaston Ashes Test which starts on Thursday, won the toss and decided to put Sussex into bat.
Keith Barker struck first for Warwicks to remove Goodwin caught by Ant Botha for 12.
The second came with Sussex having taken their score on to 75 with Wright who had made 38 from 41 balls caught by Jim Troughton. Four runs later, Rikki Clarke had Hamilton Brown (27) caught.
Boyd Rankin bowled Hodd but the other wickets to fall were all thanks to runs out and left Sussex at the end of their twenty overs on 152-9.
Jon Trott hit 56 for Warwicks but a steady fall of wickets lead to an early demise. Neil Carter made two, Jim Troughton five and Tim Ambrose one all went cheaply.
Ian Westwood who hit Warwicks only six of the innings made nineteen but after he was was, wickets continued to fall.
Frost and Clarke both made six, Ant Botha three, Rikki Clarke eight with Stefan Piolet and Boyd Rankin both making three to see Warwicks all out for 114.
On Friday, Warwicks travel to Worcester for a County Championship game. Play is due to start at New Road at 11am.