  We present a search for the pair-production of a non-standard-model
strongly-interacting particle that decays to a pair of quarks or gluons,
leading to a final state with four hadronic jets. We consider both non-resonant
production via an intermediate gluon as well as resonant production via a
distinct non-standard-model intermediate strongly-interacting particle. We use
data collected by the CDF experiment in proton-antiproton collisions at
$\sqrt{s}=1.96$ TeV corresponding to an integrated luminosity of 6.6 fb$^{-1}$.
We find the data to be consistent with standard model predictions. We report
limits on $\sigma(p\bar{p}\rightarrow$ {\it jjjj}$)$ as a function of the
masses of the hypothetical intermediate particles. Upper limits on the
production cross sections for non-standard-model particles in several resonant
and non-resonant processes are also derived.
