We report on a search for $R$-parity-violating supersymmetry in $p\overline{p}$ collisions at $\sqrt{s}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1.8\mathrm{TeV}$ using the D0 detector at Fermilab. Events with at least two electrons and four or more jets were studied. We observe two events in $99\ifmmode\pm\else\textpm\fi{}4.4{\mathrm{pb}}^{\ensuremath{-}1}$ of data, consistent with the expected background of $1.8\ifmmode\pm\else\textpm\fi{}0.4$ events. This result is interpreted within the framework of minimal low-energy supergravity supersymmetry models. Squarks with mass below $243\mathrm{GeV}/{c}^{2}$ and gluinos with mass below $227\mathrm{GeV}/{c}^{2}$ are excluded at the $95%$ C.L. for ${A}_{0}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0$, $\ensuremath{\mu}<0$, $\mathrm{tan}\ensuremath{\beta}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}2$, and a finite value for any one of the six $R$-parity-violating couplings ${\ensuremath{\lambda}}_{1jk}^{\ensuremath{'}}$ ( $j\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1$, 2 and $k\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1$, 2, 3).