Laser plasma interaction experiments have been performed using an fs Titanium Sapphire laser. Plasmas have been generated from planar PMMA targets using single laser pulses with 3.3 mJ pulse energy, 50 fs pulse duration at 800 nm wavelength. The electron density distributions of the plasmas in different delay times have been characterized by means of Nomarski Interferometry. Experimental data were compared with hydrodynamic simulation. First results to characterize the plasma density and temperature as a function of space and time are obtained. This work aims to generate plasmas in the warm dense matter (WDM) regime at near solid-density in an ultra-fast laser target interaction process. Plasmas under these conditions can serve as targets to develop X-ray Thomson scattering as a plasma diagnostic tool, e.g., using the Vacuum ultraviolet (VUV) free-electron laser (FLASH) at Dentsches Elektronen-Synchrotron (DESY) Hamburg.