There are actually two options. The other one is gaining enough reputation to have the edit priviledge. Once you have it, you can submit even one-character edits which are always applied immediately.
But going back to those below the edit priviledge. Because it is very unlike that the six-character limit will fall (there are quite a few discussions on meta.SE about it) you’ll unfortunately have to live with it and make the best out of it.
One option is certainly to rephrase the sentences around the quote if any. It is better to have a leading sentence such as ‘… as you can see in the following example’ rather than having a quotation block break up a sentence.
Another option for those who care is to additionally edit apostrophes, dashes and quotation marks (where required and applicable) to their typographic variants. Although this is a tiny bit discouraged if there is nothing else to edit in a post. And finally, there might also be the odd misspelt word that you can correct.
If all else fails, I have heard the workaround of writing
— which luckily happens to be six characters long — into the source code in a position where it doesn’t matter. But circumventing the restriction should be the last method if used at all.