The Law Code of Yājñavalkya 3.1.24

3.1.24

na vipraṃ sveṣu tiṣṭhatsu mṛtaṃ śūdreṇa hārayet |
asvargyā hy āhutiḥ sā syāc chūdrasaṃparkadūṣitā ||
(MDh 5.104)

"When his own [kinsmen] are present, one should not have a dead Brahmin carried by a Shudra;
for that offering would not lead to heaven, being defiled by contact with a Shudra." (MDh 5.104)