To solve the optimization problem described, we will use the Gurobi Python interface. The problem involves maximizing an objective function that combines milligrams of vitamin E, A, and zinc, subject to several constraints related to kidney support and digestive support indices.

First, let's break down the problem:

- Objective Function: Maximize \(6 \times \text{milligrams of vitamin E} + 3 \times \text{milligrams of vitamin A} + 3 \times \text{milligrams of zinc}\).
- Variables:
  - \(x_0\): milligrams of vitamin E
  - \(x_1\): milligrams of vitamin A
  - \(x_2\): milligrams of zinc
- Constraints:
  - Kidney support index constraints
  - Digestive support index constraints
  - Integer constraints for \(x_0\) and \(x_1\), but \(x_2\) can be fractional.

Let's translate these into Gurobi code:

```python
from gurobipy import *

# Create a model
m = Model("Vitamins_Optimization")

# Define variables
x0 = m.addVar(vtype=GRB.INTEGER, name="milligrams_of_vitamin_E")
x1 = m.addVar(vtype=GRB.INTEGER, name="milligrams_of_vitamin_A")
x2 = m.addVar(vtype=GRB.CONTINUOUS, name="milligrams_of_zinc")

# Objective function
m.setObjective(6*x0 + 3*x1 + 3*x2, GRB.MAXIMIZE)

# Constraints based on the given problem description
# Kidney support index constraints
m.addConstr(x0 + 2*x1 + x2 <= 121, name="kidney_support_index_total")
m.addConstr(2*x1 + x2 <= 121, name="kidney_support_index_vitamin_A_and_zinc")

# Digestive support index constraints
m.addConstr(21*x0 + 16*x2 >= 39, name="digestive_support_index_E_and_zinc_min")
m.addConstr(20*x1 + 16*x2 >= 33, name="digestive_support_index_A_and_zinc_min")
m.addConstr(21*x0 + 20*x1 + 16*x2 <= 133, name="digestive_support_index_total_max")
m.addConstr(21*x0 + 16*x2 <= 133, name="digestive_support_index_E_and_zinc_max")

# Solve the model
m.optimize()

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

This code defines the optimization problem as per your description and solves it using Gurobi. The model includes all specified constraints, including integer requirements for vitamin E and A quantities, and continuous (possibly fractional) quantity for zinc. The objective is to maximize the weighted sum of these vitamins/zinc quantities under the given constraints.