Résumé
Relatively light stops in gauge mediation models are usually made compatible with the Higgs mass of 125 GeV by introducing direct Higgs-messenger couplings. We show that such couplings are not necessary in a simple and predictive model that combines minimal gauge mediation and the next-to-minimal supersymmetric standard model (NMSSM). We show that one can obtain a 125 GeV Standard Model-like Higgs boson with stops as light as 1.1 TeV, thanks to the mixing of the Higgs with a singlet state at ${\cal O}(90-100)$ GeV that can explain the LEP excess. In this scenario the singlet-higgs-higgs superfields coupling $\lambda$ is small and $\tan\beta$ large. Sparticle searches at the LHC may come with additional $b-$jets or taus and may involve displaced vertices. The sparticle production cross-section at the 13 TeV LHC can be ${\mathcal O}(10-100)$ fb, leading to great prospects for discovery in the early phase of LHC Run II.