We extend the binary Fibonacci code to $d$-ary codes, with $d\ge 2$.
This is motivated by future technological developments in which the basic unit of storage will not be just a 2-valued bit, but possibly an element that is able to distinguish between $d$ different values.
The proposed codes are prefix-free, complete and more robust than Huffman codes. Experimental results illustrate that the compression efficiency of non-binary Fibonacci codes are very close to the savings achieved by the corresponding non-binary Huffman coding of the same order.