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Optical atomic clocks using highly-charged ions hold an intriguing promise ofmetrology at the 19th significant figure. Here we study transitions within the$4f^{12}$ ground-state electronic configuration of highly charged ions. Weconsider isotopes lacking hyperfine structure and show that the detrimentaleffects of coupling of electronic quadrupole moments to gradients of trappingelectric field can be effectively reduced by using specially chosen virtualclock transitions. The estimated systematic fractional clock accuracy is shownto be below $10^{-19}$.

High-precision atomic clocks with highly charged ions: nuclear spin-zero $f^{12}$-shell ions