Is your website created in html or are you using a static generator to create your website and then using gitlab pages to host it?

In the .gitlab-ci.yml file, the artifacts need to be public (even if your repository is private) for hosting your website using gitlab pages.

Here are some examples of what your .gitlab-ci.yml file needs to look like for hosting your site with gitlab pages.

HTML

pages:
  stage: deploy
  script:
  - mkdir .public
  - cp -r * .public
  - mv .public public
  artifacts:
    paths:
    - public
  only:
  - master

Jekyll

image: ruby:2.3

pages:
  stage: deploy
  script:
  - gem install jekyll
  - jekyll build -d public/
  artifacts:
    paths:
    - public
  only:
  - master

Hexo

image: node:4.2.2

pages:
  cache:
    paths:
    - node_modules/

  script:
  - npm install hexo-cli -g
  - npm install
  - hexo deploy
  artifacts:
    paths:
    - public
  only:
  - master

You should check out https://gitlab.com/pages/ which has examples of static sites created using all the different static site generator and hosted using gitlab pages.

You can also find some Jekyll themes hosted on gitlab pages at https://gitlab.com/groups/jekyll-themes

Finally, the link to your gitlab project url: https://gitlab.com/gpecchio/BeCall is private.