The phrase "impenetrable wall" refers to a wall that cannot be breached or entered. It suggests that something is so strong or secure that nothing can pass through or get past it. Full definition
I'll never forget seeing the armed police guards constantly posted at my Metro stop, getting swabbed for Anthrax (Bacillus anthracis bacteria) after setting foot in my local post office, enduring countless Code Red (i.e., severe) Homeland Security Advisor System warnings to tape my windows shut, and witnessing the massive hole bored deep into the seemingly impenetrable walls of the Pentagon during my drive to work. (patrickmahaney.com)