it's false, that quantum can break sha 256
To stay 128-bit secure against collisions all hash functions must have at least 384-bit length in post-quantum epoch. If collisions are allowed and only invertibility needs to be preserved then 256-bit length is fine.
Do you mean to truncate SHA 512 output value to get SHA 384 (192-bit security)? Why do not just try to use SHA 512 (256-bit security) to against the collisions attack?
I've read some news if SHA 256 already quantum resistance.