In most digital communication systems, error correcting codes are essential to achieve good immunity against channel impairment. Due to the complexity of the encoding process, but especially of the decoding process, most research on error correcting codes is restricted to binary data which are elements of the Galois field GF(2). Reed Solomon codes have been the most used so far as non-binary (GF(q)) error correcting codes. Recently, low complexity decoding algorithms for non-binary LDPC and non-binary turbo-codes have been developed. In this paper, the design of convolutional codes over the non-binary Galois field, with cardinal 2m (GF(2m)), is presented in order to blind identify their parameters. An extension of our blind identification method dedicated to convolutional codes over GF(2) is developed for convolutional encoders over GF(2m). Finally, the impact of Galois field parameters on the blind estimation of convolutional encoder parameters over GF(2m) is investigated.