Photonic jet is a narrow, highly intensive, weak-diverging beam propagating into a background medium, and can be produced by a cuboid solid immersion lens (SIL) in both transmission and reflection modes. Amplitude mask apodization is an optical method to further improve the spatial resolution of a SIL imaging system via reduction of waist size of photonic jet, but always leading to intensity-loss due to central masking of the incoming plane wave. In this letter, we report a particularly sized millimetre-wave cuboid SIL with the intensity-enhanced amplitude mask apodization for the first time. It is able to simultaneously deliver extra intensity enhancement and waist narrowing to the produced photonic jet. Both numerical simulation and experimental verification of the intensity-enhanced apodization effect are demonstrated using a copper-masked Teflon cuboid SIL with 22 mm side length under radiation of a plane wave with 8 mm wavelength. Peak intensity enhancement and the lateral resolution of the optical system increase by about 36.0 % and 36.4 % in this approach, respectively.