The axion is an intriguing dark matter candidate emerging from the Peccei-Quinn solution to the strong CP problem. Current experimental searches for axion dark matter focus on the axion mass range below 40 $mu$eV. However, if the Peccei-Quinn symmetry is restored after inflation the observed dark matter density points to an axion mass around 100 $mu$eV. A new project based on axion-photon conversion at the transition between different dielectric media is presented. By using $sim 80$ dielectric discs, the emitted power could be enhanced by a factor of $sim 10^5$ over that from a single mirror (flat dish antenna). Within a 10 T magnetic field, this could be enough to detect $sim 100 mu$eV axions with HEMT linear amplifiers. The design for an experiment is proposed. Results from noise, transmissivity and reflectivity measurements obtained in a prototype setup are presented. The expected sensitivity is shown.