The terrain mesh for the QR pattern is a Smooved surface (it has invisible diagonals in each square)
You'll need to select it all and Soften/Smoothe it to UNsoften the edges. Then (if you have it) you can run ThomThom's Cleanup script to merge coplanar faces and remove stray line...otherwise you'll have to delete them manually. After that, you can Push-Pull entire blocks of black squares.
Edit: I didn't realise you needed to extrude the pattern to 3D. In which case...rather than using the terrain tool, it might be easier to simply draw a square, then copy/array it 20 times laterally, then the entire line 20 times vertically. That way you'll avoid all the diagonals.