## Step 1: Define the variables and their attributes
We have four variables: 'squash plants', 'boxwoods', 'zucchini vines', and 'basil plants'. Let's denote them as $s$, $b$, $z$, and $d$ respectively. Each variable has attributes related to resilience index and yield.

## 2: Formulate the objective function
The objective function to maximize is:
\[ 6s^2 + 4sb + 7sz + 7sd + 5b^2 + 6z^2 + 4zd + 5d^2 + 2s + 9b + 6z + 8d \]

## 3: Define the constraints
1. Resilience index of squash plants: $0.7s$
2. Yield of squash plants: $0.74s$
3. Resilience index of boxwoods: $0.34b$
4. Yield of boxwoods: $0.76b$
5. Resilience index of zucchini vines: $0.18z$
6. Yield of zucchini vines: $0.55z$
7. Resilience index of basil plants: $0.46d$
8. Yield of basil plants: $0.84d$
9. $s + d \geq 13$
10. $z + d \geq 5$
11. $b^2 + d^2 \geq 11$
12. $0.74s + 0.55z \geq 11$
13. $0.76b + 0.55z \geq 10$
14. $-4s^2 + 7z^2 \geq 0$
15. $0.34b + 0.46d \leq 35$
16. $0.7s + 0.18z \leq 18$
17. $0.7s + 0.46d \leq 36$
18. $0.7^2s^2 + 0.34^2b^2 \leq 10$
19. $0.7s + 0.34b + 0.18z + 0.46d \leq 10$
20. $0.76b + 0.55z \leq 36$
21. $0.74s + 0.55z \leq 21$
22. $0.76b + 0.84d \leq 16$
23. $0.74s + 0.76b \leq 24$
24. $0.74s + 0.84d \leq 35$
25. $0.74s + 0.76b + 0.55z + 0.84d \leq 35$
26. $s, b, z, d$ are integers.

## 4: Implement the problem in Gurobi
```python
import gurobi

# Create a new Gurobi model
m = gurobi.Model()

# Define the variables
s = m.addVar(name="squash_plants", vtype=gurobi.GRB.INTEGER)
b = m.addVar(name="boxwoods", vtype=gurobi.GRB.INTEGER)
z = m.addVar(name="zucchini_vines", vtype=gurobi.GRB.INTEGER)
d = m.addVar(name="basil_plants", vtype=gurobi.GRB.INTEGER)

# Objective function
m.setObjective(6*s**2 + 4*s*b + 7*s*z + 7*s*d + 5*b**2 + 6*z**2 + 4*z*d + 5*d**2 + 2*s + 9*b + 6*z + 8*d, gurobi.GRB.MAXIMIZE)

# Constraints
m.addConstr(s + d >= 13)
m.addConstr(z + d >= 5)
m.addConstr(b**2 + d**2 >= 11)
m.addConstr(0.74*s + 0.55*z >= 11)
m.addConstr(0.76*b + 0.55*z >= 10)
m.addConstr(-4*s**2 + 7*z**2 >= 0)
m.addConstr(0.34*b + 0.46*d <= 35)
m.addConstr(0.7*s + 0.18*z <= 18)
m.addConstr(0.7*s + 0.46*d <= 36)
m.addConstr((0.7*s)**2 + (0.34*b)**2 <= 10)
m.addConstr(0.7*s + 0.34*b + 0.18*z + 0.46*d <= 10)
m.addConstr(0.76*b + 0.55*z <= 36)
m.addConstr(0.74*s + 0.55*z <= 21)
m.addConstr(0.76*b + 0.84*d <= 16)
m.addConstr(0.74*s + 0.76*b <= 24)
m.addConstr(0.74*s + 0.84*d <= 35)
m.addConstr(0.74*s + 0.76*b + 0.55*z + 0.84*d <= 35)

# Optimize the model
m.optimize()

# Print the solution
if m.status == gurobi.GRB.OPTIMAL:
    print("Objective: ", m.objVal)
    print("Squash plants: ", s.varValue)
    print("Boxwoods: ", b.varValue)
    print("Zucchini vines: ", z.varValue)
    print("Basil plants: ", d.varValue)
else:
    print("The model is infeasible")
```