Hamming Quasi-cyclic (HQC) is an alternate candidate at the NIST call for proposal. Before standardization, the NIST expects studies about Side-Channel Attacks (SCA) for the third round schemes. This paper introduces an horizontal attack against the Reed-Solomon (RS) decoding algorithm of HQC assuming an Hamming weight leakage model. The aim of the attack is to recover the RS codeword generated directly related to the exchanged message with no more knowledge than public codes and parameters of the scheme. This attack targets the syndrome computation of the RS decoder where an error-free codeword is manipulated. The public RS decoder algorithm allows to correct the erroneous inferred bytes from SCA. By using list decoding algorithms, we increase the error correction capability and the strength of the attack. Then we give an analysis based on simulated traces. In practice, experiments show that the measured signal to noise ratio is sufficiently low for a successful attack against the reference implementation of HQC$128$ by running $2^{96}$ operations over a Galois field. Finally, we present a random shuffling countermeasure in order to prevent this horizontal attack.