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~ Viewing the codewords of an [n, k ] linear code over a field Fqm as m x n matrices over Fq by expanding each entry of the codeword with respect to an Fq-basis of Fqm, the rank weight of a codeword is the rank over Fq of the corresponding matrix and the rank of the code is the minimum rank weight among all non-zero codewords. For m 2 n -k + l , codes with maximum possible rank distance, called Maximum Rank Distance (MRD) codes have been studied previously. In this paper, we study codes with maximum possible rank distance for the cases m 5 n -k + 1, calling them Full Rank Distance (FRD) codes. Generator matrices of FRD codes are characterized.