I'm not sure that I understand the instruction in this puzzle. Is the following interpretation of the problem correct?
1) A number N is chosen, where N is larger than the largest number in the cipher code.
2) The fibonnaci series F(i) modulo N has a period of 26, meaning that for any index i, F(i) mod N == F(i + 26) mod N
3) The list of 26 values from within 1 period is sorted in ascending order, and each number assigned a letter according to its ordinal index (smallest number is A, second smallest is B, and so on).
4) This transformation is then applied to "Gardening is just a soil sport" to get ( 3 0 89 1 2 34 5 34 3/ 5 144 / 8 377 144 233 / 0 / 144 34 5 13 /144 55 34 89 233 )
5) Find N
PS. Also, does this sequence start at 1 or 0? Many references for the fibonnacci series start at 0.