Ok now I get what you mean with separable.
I now have two different switchable blurs implemented, the gaussian blur and one where I simply use the weights {0.25,0.5,0.75,1,...,1,0.75,0.5,0.25} (and divide by their sum). It works quite well with the blocky geometry and both blurs look much nicer than my previous box blur, so thank you very much for the tip!