To achieve convincing remote vibrotactile experiences, it is necessary to transmit a large number of signal channels corresponding to dense interaction points on the human skin. This leads to a dramatic increase in the amount of data to be transmitted. In order to cope with these data efficiently, vibrotactile codecs have to be used to reduce the data rate demands. Although first vibrotactile codecs have been introduced in the past, they are mostly single-channel codecs and cannot achieve the required data reduction. Therefore, in this paper, a multi-channel vibrotactile codec is presented that extends a wavelet-based codec for single channel signals. By leveraging interchannel redundancies using channel clustering and differential coding, the presented codec is able to achieve a reduction of 69.1% in data rate compared to the state-of-the-art single-channel codec while maintaining a perceptual ST-SIM quality score of 95%.