I have to evaluate many 20 character strings.  How would I only allow a match for strings that do not end with four or more zeros?

Basic alphanumeric strings.  

Case doesn't matter.

Given the following strings:

00000000000234560000

F0000000001234560R00

000000000012d4500000

00030000001234560200

0000000000s234560000

00000FF000324400000E

The result would be

00030000001234560200

F0000000001234560R00

00000FF000324400000E

I was trying

^.+([^0]|[^0][0]|[^0][0][0]|[^0][0][0][0])$

but it didn't seem to product expected results.

 Any help is most appreciated.