A two-dimensional (2D) solid-state random laser emitting in the visible is demonstrated, in which optical feedback is provided by a controlled disordered arrangement of air-holes in a dye-doped polymer film. We find an optimal scatterer density for which threshold is minimum and scattering is the strongest. We show that the laser emission can be red-shifted by either decreasing scatterer density or increasing pump area. We show that spatial coherence is easily controlled by varying pump area. Such a 2D random laser provides with a compact on-chip tunable laser source and a unique platform to explore non-Hermitian photonics in the visible.