The Indy Autonomous Challenge (IAC) brought together for the first time in history nine autonomous racing teams competing at an unprecedented speed and in a head-to-head scenario, using independently developed software on open-wheel race cars. This paper presents the complete software architecture used by the team TII EuroRacing (TII-ER), covering all the modules needed to avoid static obstacles, perform active overtakes, and reach speeds above 75 m/s (270 km/h). In addition to the most common modules related to perception, planning, and control, we discuss the approaches used for vehicle dynamics modeling, simulation, telemetry, and safety. Overall results and the performance of each module are described, as well as the lessons learned during the first two events of the competition on oval tracks, where the team placed second and third, respectively.