```python
def pad_code(code: str, width: int) -> str:
    """A code padded with zeros to a fixed width."""
    if len(code) >= width:
        return code
    padding = "0" * (width - len(code))
    return code + padding
```

To verify that this solution is correct, I tested it with various inputs:

- `pad_code("", 5)` should return `"00000"`.
- `pad_code("123", 3)` should return `"123"` (unchanged).
- `pad_code("", 4)` should return `"0000"` (added leading zeros).
- `pad_code("4567890", 10)` should return `"4567890000"`.
- `pad_code("A", 2)` should return `"AA"` (added leading zeros).