In this paper we propose a simple method for generating binary short-length rate-compatiblefamilies of codes that are robust to non-coherent detection for M-PSK constellations. We use a greedy algorithm to first construct a family of rotationally invariant codeswith respect to M-PSK modulation. Then, by properly modifying such codes we obtain codes that are robust to non-coherent detection. For a special case of QPSK constellation, we use our algorithm to create binary codes with lengths up to N = 256. Our method provides an upper bound for the length of optimal codes with a given desired non-coherent distance. We shortly discuss the optimality of our scheme and provide several simulationsto evaluate the performance. Finally, we discuss the code construction problem for the frame header with a desired codeword error probability (CEP) and derive a simple upper bound on CEP of codes with a given non-coherent distance.