To solve this optimization problem, we first need to define the variables, the objective function, and the constraints using Gurobi's Python API.

### Problem Description

The problem involves maximizing an objective function subject to several constraints. The variables are:
- `vincas`
- `tomato vines`
- `strawberry bushes`
- `ferns`

The objective function to maximize is:
\[ 4 \cdot vincas^2 + 9 \cdot vincas \cdot tomato\ vines + 9 \cdot vincas \cdot strawberry\ bushes + 4 \cdot vincas \cdot ferns + 9 \cdot tomato\ vines \cdot strawberry\ bushes + 6 \cdot strawberry\ bushes^2 + 6 \cdot strawberry\ bushes \cdot ferns + 4 \cdot ferns^2 + 2 \cdot tomato\ vines \]

Subject to constraints on costs and expenditures.

### Gurobi Code

```python
import gurobi

def solve_optimization_problem():
    # Create a new Gurobi model
    model = gurobi.Model()

    # Define variables
    vincas = model.addVar(name="vincas", vtype=gurobi.GRB.INTEGER)
    tomato_vines = model.addVar(name="tomato_vines", vtype=gurobi.GRB.INTEGER)
    strawberry_bushes = model.addVar(name="strawberry_bushes", vtype=gurobi.GRB.INTEGER)
    ferns = model.addVar(name="ferns", vtype=gurobi.GRB.INTEGER)

    # Objective function
    model.setObjective(4 * vincas**2 + 9 * vincas * tomato_vines + 9 * vincas * strawberry_bushes + 
                       4 * vincas * ferns + 9 * tomato_vines * strawberry_bushes + 
                       6 * strawberry_bushes**2 + 6 * strawberry_bushes * ferns + 
                       4 * ferns**2 + 2 * tomato_vines, gurobi.GRB.MAXIMIZE)

    # Constraints
    model.addConstr(2 * vincas + 1 * tomato_vines + 10 * strawberry_bushes + 9 * ferns <= 92, "Budget_Constraint")
    model.addConstr(2 * vincas + 9 * ferns >= 12, "Vincas_Ferns_Min_Constraint")
    model.addConstr(vincas**2 + strawberry_bushes**2 >= 22, "Vincas_Strawberry_Min_Squared_Constraint")
    model.addConstr(1 * tomato_vines + 10 * strawberry_bushes >= 9, "Tomato_Strawberry_Min_Constraint")
    model.addConstr(2 * vincas + 1 * tomato_vines >= 11, "Vincas_Tomato_Min_Constraint")
    model.addConstr(strawberry_bushes**2 + ferns**2 >= 14, "Strawberry_Ferns_Min_Squared_Constraint")
    model.addConstr(vincas**2 + strawberry_bushes**2 + ferns**2 >= 17, "Vincas_Strawberry_Ferns_Min_Squared_Constraint")
    model.addConstr(vincas**2 + tomato_vines**2 + strawberry_bushes**2 >= 17, "Vincas_Tomato_Strawberry_Min_Squared_Constraint")
    model.addConstr(2 * vincas + 10 * strawberry_bushes + 9 * ferns >= 12, "Vincas_Strawberry_Ferns_Total_Min_Constraint")
    model.addConstr(vincas**2 + tomato_vines**2 + strawberry_bushes**2 >= 12, "Vincas_Tomato_Strawberry_Squared_Min_Constraint")
    model.addConstr(2 * vincas + 10 * strawberry_bushes <= 58, "Vincas_Strawberry_Max_Constraint")
    model.addConstr(vincas**2 + tomato_vines**2 <= 49, "Vincas_Tomato_Squared_Max_Constraint")
    model.addConstr(1 * tomato_vines + 10 * strawberry_bushes <= 27, "Tomato_Strawberry_Max_Constraint")
    model.addConstr(10 * strawberry_bushes**2 + 9 * ferns**2 <= 82, "Strawberry_Ferns_Squared_Max_Constraint")
    model.addConstr(2 * vincas + 9 * ferns <= 36, "Vincas_Ferns_Max_Constraint")
    model.addConstr(1 * tomato_vines + 9 * ferns <= 69, "Tomato_Ferns_Max_Constraint")
    model.addConstr(2 * vincas + 1 * tomato_vines + 10 * strawberry_bushes + 9 * ferns <= 69, "Total_Max_Constraint")

    # Optimize the model
    model.optimize()

    # Print the solution
    if model.status == gurobi.GRB.OPTIMAL:
        print("Objective: ", model.objVal)
        print("Vincas: ", vincas.varValue)
        print("Tomato Vines: ", tomato_vines.varValue)
        print("Strawberry Bushes: ", strawberry_bushes.varValue)
        print("Ferns: ", ferns.varValue)
    else:
        print("The model is infeasible")

solve_optimization_problem()
```