Is it possible to install another version of Python to Virtualenv?

I have a shared account in a web-hosting that has Python 2.4 installed, but my code is not compatible with 2.4. Is it possible to install Python 2.6 directly to Virtualenv?

Note: I don´t have permission to install it in the shared server.

Here are the options for virtualenv

$ virtualenv
You must provide a DEST_DIR
Usage: virtualenv [OPTIONS] DEST_DIR

Options:
  --version             show program's version number and exit.
  -h, --help            show this help message and exit.
  -v, --verbose         Increase verbosity.
  -q, --quiet           Decrease verbosity.
  -p PYTHON_EXE, --python=PYTHON_EXE
                        The Python interpreter to use, e.g.,
                        --python=python2.5 will use the python2.5 interpreter
                        to create the new environment.  The default is the
                        interpreter that virtualenv was installed with
                        (/usr/bin/python)
  --clear               Clear out the non-root install and start from scratch
  --no-site-packages    Don't give access to the global site-packages dir to
                        the virtual environment
  --unzip-setuptools    Unzip Setuptools or Distribute when installing it
  --relocatable         Make an EXISTING virtualenv environment relocatable.
                        This fixes up scripts and makes all .pth files
                        relative
  --distribute          Use Distribute instead of Setuptools. Set environ
                        variable VIRTUALENV_USE_DISTRIBUTE to make it the
                        default
  --prompt==PROMPT      Provides an alternative prompt prefix for this
                        environment

1) What you want to do is install python to a directory that you are able to write too.

You can follow the instructions here.

For Python 2.7.1
Python source

mkdir ~/src
mkdir ~/.localpython
cd ~/src
wget http://www.python.org/ftp/python/2.7.1/Python-2.7.1.tgz
tar -zxvf Python-2.7.1.tgz
cd Python-2.7.1

make clean
./configure --prefix=/home/${USER}/.localpython
make
make install

2) Install virtualenv
virtualenv source

cd ~/src
wget http://pypi.python.org/packages/source/v/virtualenv/virtualenv-1.5.2.tar.gz#md5=fbcefbd8520bb64bc24a560c6019a73c
tar -zxvf virtualenv-1.5.2.tar.gz
cd virtualenv-1.5.2/
~/.localpython/bin/python setup.py install

3) Create a virtualenv using your local python
virtualenv docs

mkdir /home/${USER}/virtualenvs
cd /home/${USER}/virtualenvs
~/.localpython/bin/virtualenv py2.7 --python=/home/${USER}/.localpython/bin/python2.7

4) Activate the environment

cd ~/virtualenvs/py2.7/bin
source ./activate

5) Check

(py2.7)$ python
Python 2.7.1 (r271:86832, Mar 31 2011, 15:31:37) 
[GCC 4.4.5] on linux2
Type "help", "copyright", "credits" or "license" for more information.
>>> exit()

(py2.7)$ deactivate
$ python
Python 2.6.6 (r266:84292, Sep 15 2010, 15:52:39) 
[GCC 4.4.5] on linux2
Type "help", "copyright", "credits" or "license" for more information.
>>>