Single-ion sensitivity is obtained in precision Penning-trap experiments devoted to light (anti)particles or ions with low mass-to-charge ratios, by adding an inductance coil to an amplifier connected to the trap, both operated at 4 K. However, single-ion sensitivity has not been reached on heavy singly or doubly charged ions. In this publication, we present a new system to reach this point, based on the use of a quartz crystal as an inductance, together with a newly developed broad-band (BB) amplifier. We detect the reduced-cyclotron frequency of 40Ca+ ions stored in a 7-tesla open-ring Penning trap. By comparing the detected electric signal obtained with the BB amplifier and the fluorescence signal obtained by collecting the photons emitted by a trapped ion cloud, we show a detection limit below 110 ions. Adding the crystal, the electrical signal increases by a factor of about 30 at room temperature, which combined with the measured equivalent resistance and voltage noise, proves the feasibility of the system to reach single-ion sensitivity at 4 K.