Placing gaussian function at different points on mesh

I am looking to create a random distribution of gaussian curve shapes on a large mesh. I basically want to take this function :

Z = 0.3*exp(-5*(x.^2+y.^2))-0.1;
Z(Z<0)=0;

and be able to choose its location (in x & y coords), and have multiple plots.

So at the moment, I have this:

But I would like to have this generated:

Is there a reasonably simple way to do this? I have tried to play around with the code but I am afraid I'm not a mathematics, nor a MATLAB expert.

Any help would be much appreciated.