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Almost you did it, you just only have tiny mistake instead of set 1 to entity you have to set target_id(I guest 1 is your userid ),

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

For multiple value field (to add the value to the end of the list) use:

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

another solution is set user entity object to value

So first load your user object then set it to entity property with

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

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();

Almost you did it, you just only have tiny mistake instead of set 1 to entity you have to set target_id(I guest 1 is your userid ),

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

another solution is set user entity object to value

So first load your user object then set it to entity property with

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

Almost you did it, you just only have tiny mistake instead of set 1 to entity you have to set target_id(I guest 1 is your userid ),

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

For multiple value field (to add the value to the end of the list) use:

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

another solution is set user entity object to value

So first load your user object then set it to entity property with

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

Almost you did it, you just only have tiny mistake instead of set 1 (I think 1 is your userid ), you should set user entity object to value

So first load your user object then set it.

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

Almost you did it, you just only have tiny mistake instead of set 1 to entity you have to set target_id(I guest 1 is your userid ),

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

another solution is set user entity object to value

So first load your user object then set it to entity property with

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