We present the results of a computer simulation study of thermodynamical properties of TIP4P water confined in a hydrophobic disordered matrix of soft spheres upon supercooling. The hydrogen-bond network of water appears preserved in this hydrophobic confinement. Nonetheless a reduction in the average number of hydrogen bonds due to the geometrical constraints is observed. The liquid branch of the spinodal line is calculated from 350 K down to 210 K. The same thermodynamic scenario of the bulk is found: the spinodal curve is monotonically decreasing. The line of maximum density bends avoiding a crossing of the spinodal. There is, however, a shift both of the line of maximum density and of the spinodal toward higher pressures and lower temperatures with respect to bulk.