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();
Example with set() method:
$node->set('field_article_images', $fid);
