We report results of a search for particles with anomalously high ionization in events with a high transverse energy jet and large missing transverse energy in $2.4$ fb$^{-1}$ of integrated luminosity collected by the D0 experiment at the Fermilab Tevatron $p\bar{p}$ collider. Production of such particles (quirks) is expected in scenarios with extra QCD-like {\it SU(N)} sectors, and this study is the first dedicated search for such signatures. We find no evidence of a signal and set a lower mass limit of 107 ~GeV for the mass of a charged quirk with strong dynamics scale $\Lambda$ in the range from 10 keV to 1 MeV.