  We present a class of models in the framework of gauge mediation
supersymmetry breaking where the messenger fields transform in the adjoint
representation of the Standard Model gauge symmetry. To avoid unacceptably
light right-handed sleptons in the spectrum we introduce a non-zero U(1)_B-L
D-term. This leads to an additional contribution to the soft supersymmetry
breaking mass terms which makes the right-handed slepton masses compatible with
the current experimental bounds. We show that in this framework the observed
125 GeV Higgs boson mass can be accommodated with the sleptons accessible at
the LHC, while the squarks and gluinos lie in the multi-TeV range. We also
discuss the issue of the fine-tuning and show that the desired relic dark
matter abundance can also be accommodated.
