The glassy state of several concentrations of propylene glycol in D2O is presently characterized by enthalpy relaxation experiments. The existence of a lowest glass transition temperature T-s has defined an utmost excess enthalpy that can be stored by the glass during cooling. Similar to the thermal behavior of the shear viscosity for liquids, these T-s values are maximum for the binary system with compositions in the range 78-82% (w/w) propylene glycol in D2O, suggesting that these concentrations correspond to the strongest glasses, and provide a higher thermodynamic strength for these glasses. These glasses correspond also to the maximum excess enthalpy that can be stored by the glassy state during cooling. These concentrations present, however, an apparent minimum threshold stress to induce fracture nucleation in the glasses with the definition of a maximum mechanical fragility. The present results underline a problem in the definition of the thermodynamic and mechanical strength of the glassy state as an extension of the fragility definition for liquids.