 Here is a simplified Python code that follows your instructions, using the `numpy`, `scipy`, `simsopt`, and `vtk` libraries. Please note that this is a simplified version and might need adjustments based on your specific requirements.

```python
import numpy as np
from simsopt import Problem, Objective, Variable
from scipy.optimize import minimize
from simsopt.geometries import BoundarySurface, Curve, Multifilament
from simsopt.solvers import Stellarator, RotationSymmetry
from simsopt.physics import BiotSavartLaw

# Define the problem
p = Problem()

# Define the boundary magnetic surface
boundary = BoundarySurface(np.array([[0, 0], [1, 0], [1, 1], [0, 1], [0, 0]]))

# Create equally spaced curves
n_curves = 100
curves = [Curve(boundary, t) for t in np.linspace(0, 1, n_curves)]

# Initialize multifilament pack
multifilament = Multifilament(curves, n_filaments=10)

# Apply stellarator and rotation symmetries
stellarator = Stellarator(multifilament, (0, 0, 1))
rotation = RotationSymmetry(stellarator, (0, 0, 1), 0.5)

# Define the Biot-Savart law
law = BiotSavartLaw(rotation)

# Define the objective function
def obj_func(x):
    multifilament.set_positions(x)
    flux = np.sum(law.flux_density(multifilament)) ** 2
    curve_length = np.sum([curve.length() for curve in multifilament.curves])
    distance = np.sum([(multifilament[i] - multifilament[j]).norm() for i in range(len(multifilament)) for j in range(i+1, len(multifilament))])
    return flux + 10 * curve_length + distance

# Define the variables
x0 = np.random.uniform(low=-0.1, high=0.1, size=(len(multifilament) * 3))
variables = [Variable(name=f"x{i}", lower=-0.1, upper=0.1) for i in range(len(x0))]

# Define the optimization problem
p.objective = Objective(obj_func)
p.variables = variables

# Perform the optimization
result = minimize(p.objective, x0, method='L-BFGS-B', jac=p.jacobian, options={'maxiter': 1000})

# Save the result in VTK format
import vtk
writer = vtk.vtkPolyDataWriter()
writer.SetInputData(multifilament.polydata)
writer.SetFileName('optimized_coil.vtk')
writer.Write()
```

This code creates a coil optimization problem with a multifilament approach, using the simsopt library. The objective function is a combination of the squared flux, curve length penalty, and coil-to-coil distance penalty. The code initializes the boundary magnetic surface, creates equally spaced curves and multifilament grid, applies stellarator and rotation symmetries, defines the Biot-Savart law, and performs the optimization using the L-BFGS-B method from scipy.optimize. The output is saved in VTK format.