MSSM with $m_h=125$ GeV in High-Scale Gauge Mediation

After the discovery of SM-like Higgs with $m_h=125$ GeV, it is increasingly urgent to explore a solution to the hierarchy problem. In the context of MSSM from gauge-mediated SUSY breaking, the lower bound on gluino mass suggests that the messenger scale $M$ is probably large if the magnitude of $\mathrm{\Lambda }\sim 100$ TeV. In this paper, we study $\bar{\mathbf{5}}+\mathbf{5}$ model with $M\sim {10}^8-{10}^{12}$ GeV and $\mathrm{\Lambda }\simeq 100$ TeV. For moderate Higgs-messenger coupling, it will be shown a viable model with moderate fine tuning. In this model, $\mu \sim 800$ GeV and $B_{\mu }$ nearly vanishes at input scale, which can be constructed in microscopic model.