An asset is a resource under the control of the company, arising from past events, the use of which will result in the inflow of economic resource capable of reliable measurement.
Does your website satisfy the component elements of the definition?
I’m not familiar with SIC 32 but would be surprised to learn that a website designed by someone other than you, and paid for, should be classed as an expense. It seems to me to satisfy all the elements fundamental to classification as an asset, but …..