Here is a simple Python code to calculate the distance between two N-dimensional vectors with a check if the vectors are of the same dimension:

```python
import math

def distance(vector1, vector2):
    # Check if both vectors have the same dimension
    if len(vector1) != len(vector2):
        return None
    
    # Calculate the sum of squared differences between each element in the vectors
    sum_of_squares = 0
    for i in range(len(vector1)):
        difference = vector1[i] - vector2[i]
        sum_of_squares += difference ** 2
    
    # Return the square root of the sum of squared differences
    return math.sqrt(sum_of_squares)
```

To use this function, simply pass in two N-dimensional vectors as arguments:

```python
vector1 = [1, 2, 3]
vector2 = [4, 5, 6]

distance_between_vectors = distance(vector1, vector2)
print(distance_between_vectors) # Output: 5.196152422706632
```

If the two vectors are not of the same dimension, the function will return `None`:

```python
vector1 = [1, 2, 3]
vector2 = [4, 5]

distance_between_vectors = distance(vector1, vector2)
print(distance_between_vectors) # Output: None
```
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