Joux presents an elegant way to generate k-way multi-collisions with about as much effort as generating a single collision: https://www.iacr.org/archive/crypto2004/31520306/multicollisions.pdf
However, so far I have only found applications of this attack on full-length hash functions like SHA-256 or MD-5. Therefore, consider this following scenario:
An attacker wants to find a 2^70-way multicollision of the first 70 bits of a SHA-256 output. In essence, the output of SHA-256 is truncated to 70 bits (let's call this function SHA-70). Can Joux's multicollision attack be applicable in this scenario? If so, how much effort would be required?