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You need to use code similar to the following.

    $node = Node::load($nid);     
    $node->field_code_used_by->target_id = $user_id;
    $node->save();

For a multiple-value field, to add the value to the end of the list, use the following code.

$node->field_code_used_by[] = ['target_id' => $user_id];

Another way is setting the entity property with the entity object, as in the following code.

    $node = Node::load($nid);
    $user = \Drupal\user\Entity\User::load(1);
    $node->field_code_used_by->entity = $user;
    $node->save();