A description is given of two new infinite families of nonlinear binary codes. For all block lengths n = 22m, m ≥ 3, two nonlinear binary codes are defined, which are called dual as their distance distributions satisfy the MacWilliams identities. The first code has minimum distance 8 and has four times as many codewords as the corresponding extended BCH code. In the other code, there are only six distinct nonzero values for the distances between codewords.