The way you state the problem, there are two regions that are bound by those surfaces, one above and one below the parabolic cylinder 4x^2 + y^2 +z = 128, as you can see from the picture:
ContourPlot3D[{4 x^2 + y^2 + z == 128, x == 0, x == 4, y == 0, y == 4},
{x, -1, 5}, {y, -1, 5}, {z, 50, 150},
ContourStyle -> Opacity[0.8], AxesLabel -> Automatic]
