@vv 
Got it, that gives a good answer. Sorry to bother you, but what if I need those polynomials not in a sequence but idividually? I need to be able to name them to proceed with other steps :(

@vv 
Thank you for your answer. Let's say I need 0<=a_i<=2 (a_i=0,1,2) and a_0<> 0. That gives exactly 54 different polynomials (polynomials are monic). I need to get all of them in the form pol[m]. How to proceed in that case?

@Kitonum 
Thanks for answer. But the issue is, that I need to choose a_i from Z, so a_i=0,1,2 and a_0 <> 0. That creates exactly 54 different quartic polynomials in this case and I need to list all of them.