Coding theory - proof from spheres

Hello all, I have just come across this forum when looking for some information regarding some problems I'm currently having some problems with.

The first question (I will post another thread for the other), regards prooving a statement using first principals and spheres in coding theory. It is described as follows:

Show that there is no 5-ary code of length 8 and distance 7 with more than 100 codewords. You should prove this from first principles using spheres and without using known bounds on the number of codewords.

I have attempted this by trying to prove the number of possible words that exist in the spheres (of radius 1) if the number of codewords were equal to (or greater than) 101, is greater than that possible and hence is a contradiction. This was to no avail however and I'm a bit stuck.

Any help is greatly appreaciated.

Thanks so much!