To solve this optimization problem, we need to translate the given objective function and constraints into a mathematical model that can be implemented using Gurobi. 

The objective function is to minimize: $3.09 \times (\text{milligrams of vitamin B6})^2 + 8.41 \times (\text{milligrams of vitamin B6}) \times (\text{milligrams of calcium}) + 2.01 \times (\text{milligrams of calcium})^2 + 8.39 \times (\text{milligrams of calcium})$.

The constraints are:
1. The immune support index of milligrams of vitamin B6 is 16.
2. Milligrams of vitamin B2 have an immune support index of 20.
3. The immune support index of milligrams of calcium is 22.
4. The total combined immune support index from milligrams of vitamin B2 and milligrams of calcium has to be greater than or equal to 52.
5. The total combined immune support index from milligrams of vitamin B6, milligrams of vitamin B2, and milligrams of calcium has to be at minimum 52.
6. The total combined immune support index from milligrams of vitamin B6 plus milligrams of calcium must be equal to or less than 101.

Let's denote:
- $x_0$ as the quantity of milligrams of vitamin B6,
- $x_1$ as the quantity of milligrams of vitamin B2, and
- $x_2$ as the quantity of milligrams of calcium.

From the problem description, we have specific coefficients for each type of vitamin/mineral in terms of immune support index:
- For vitamin B6: 16,
- For vitamin B2: 20,
- For calcium: 22.

Now, let's write down the mathematical formulation based on these definitions and constraints:

Minimize $3.09x_0^2 + 8.41x_0x_2 + 2.01x_2^2 + 8.39x_2$

Subject to:
- $16x_0 \leq 201$ (since the upper bound for immune support index from vitamin B6 is not directly given but we have an upper bound for 'r0' which seems unrelated, this constraint might need adjustment based on actual problem intent),
- $20x_1 + 22x_2 \geq 52$,
- $16x_0 + 20x_1 + 22x_2 \geq 52$,
- $16x_0 + 22x_2 \leq 101$.

Since the problem does not specify an upper bound for vitamin B6, B2, or calcium directly in terms of their quantities but mentions 'r0' which seems to be a mix-up, we will ignore the 'upper_bound': 201 as it's unclear how it applies without further context. 

Given $x_1$ must be a whole number and $x_0$, $x_2$ can be non-whole numbers, our model should account for integer constraints on $x_1$.

```python
from gurobipy import *

# Create a new model
m = Model("Immune_Support_Optimization")

# Define variables
x0 = m.addVar(lb=0, vtype=GRB.CONTINUOUS, name="milligrams_of_vitamin_B6")
x1 = m.addVar(lb=0, vtype=GRB.INTEGER, name="milligrams_of_vitamin_B2")
x2 = m.addVar(lb=0, vtype=GRB.CONTINUOUS, name="milligrams_of_calcium")

# Objective function
m.setObjective(3.09 * x0**2 + 8.41 * x0 * x2 + 2.01 * x2**2 + 8.39 * x2, GRB.MINIMIZE)

# Constraints
m.addConstr(20*x1 + 22*x2 >= 52, name="constraint_1")
m.addConstr(16*x0 + 20*x1 + 22*x2 >= 52, name="constraint_2")
m.addConstr(16*x0 + 22*x2 <= 101, name="constraint_3")

# Optimize model
m.optimize()

# Print solution
if m.status == GRB.OPTIMAL:
    print("Optimal solution found:")
    print(f"Milligrams of Vitamin B6: {x0.x}")
    print(f"Milligrams of Vitamin B2: {x1.x}")
    print(f"Milligrams of Calcium: {x2.x}")
else:
    print("No optimal solution found")
```