A search for the doubly charmed baryon $\Omega cc+$ with the decay mode $\Omega cc+\to \Xi c+K-\pi +$ is performed using proton-proton collision data at a centre-of-mass energy of 13$\mathrm{Te}V$ collected by the LHCb experiment from 2016 to 2018, corresponding to an integrated luminosity of $5.4\mathrm{fb}-1$. No significant signal is observed within the invariant mass range of 3.6 to 4.0$\mathrm{Ge}V/c2$. Upper limits are set on the ratio $R$ of the production cross-section times the total branching fraction of the $\Omega cc+\to \Xi c+K-\pi +$ decay with respect to the $\Xi cc++\to \Lambda c+K-\pi +\pi +$ decay. Upper limits at 95% credibility level for $R$ in the range $0.005$ to $0.11$ are obtained for different hypotheses on the $\Omega cc+$ mass and lifetime in the rapidity range from 2.0 to 4.5 and transverse momentum range from 4 to 15$\mathrm{Ge}V/c$.