Conduct records are maintained separately from a student's academic transcript. These records are maintained for several years (sometimes longer, depending on the seriousness of the incident). Typically student conduct records are shared only with those college employees who have a legitimate educational interest in the information, but information may be shared based on other exceptions are listed in the College's FERPA policy.
Suspension and expulsion are the only sanctions that are designated on a transcript. If your student is determined to be responsible for violating the Student Code of Conduct, he/she may have to disclose that through application processes for other colleges/universities, background checks, or for other such purposes.
If a student wants you to have access to his/her records, a written FERPA release will need to be provided by your student.