A computer search algorithm for optimum free distance (OFD) binary convolutional codes is presented. The algorithm obtains polynomial encoders for rate-1/2 and rate-2/4 OFD binary convolutional codes. For rate-1/2 OFD binary convolutional codes, the search is done for memory 1,2,3,4 and 5 and having Hamming free distances dfree equal to 4,5,6,7 and 8, respectively. Minimal-basic encoders are also derived. The encoders for rate-2/4 OFD binary convolutional codes have memory 2 and dfree - 8 and all are minimal-basic. The resulting codes meet the Griesmer's upper bound on the free distance.