To solve this optimization problem using Gurobi, we first need to understand and translate the given natural language description into a mathematical formulation that can be represented in code.

The objective function to minimize is: $2.44 \times (\text{number of zucchini vines}) + 6.82 \times (\text{number of cucumber vines})$.

Let's denote:
- $z$ as the number of zucchini vines,
- $c$ as the number of cucumber vines.

The constraints based on the description are:

1. Resilience index constraint: $8z + 15c \geq 66$
2. Planting space constraint (minimum): $6z + c \geq 66$
3. Additional constraint: $8z - 3c \geq 0$
4. Maximum resilience index: $8z + 15c \leq 159$
5. Maximum planting space: $6z + c \leq 172$

Given that both $z$ and $c$ must be integers (whole numbers of vines), we can formulate this as a Mixed-Integer Linear Programming (MILP) problem.

Here's how the problem can be represented in Gurobi Python code:

```python
from gurobipy import *

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

# Define variables
z = m.addVar(vtype=GRB.INTEGER, name="zucchini_vines")
c = m.addVar(vtype=GRB.INTEGER, name="cucumber_vines")

# Objective function: Minimize 2.44*z + 6.82*c
m.setObjective(2.44*z + 6.82*c, GRB.MINIMIZE)

# Constraints
m.addConstr(8*z + 15*c >= 66, "resilience_min")
m.addConstr(6*z + c >= 66, "space_min")
m.addConstr(8*z - 3*c >= 0, "additional_constraint")
m.addConstr(8*z + 15*c <= 159, "resilience_max")
m.addConstr(6*z + c <= 172, "space_max")

# Optimize model
m.optimize()

# Print solution
if m.status == GRB.OPTIMAL:
    print("Optimal solution found:")
    print(f"Zucchini Vines: {z.x}")
    print(f"Cucumber Vines: {c.x}")
    print(f"Objective Function Value: {m.objVal}")
else:
    print("No optimal solution found")
```