I'm not sure specifically what data you have but it sounds like you have enough data to calculate a rough gini estimate.
Gini is equal to: (The average variance for incomes) / (2 * the mean)
Since Gini is a standardized indicator and not dependent on the level of income, just the variance, you can construct a rough gini metric using your data.
If you assume 0-25K = 0, 25K-50K = 1, 50K-75K = 2 etc. You can treat the buckets as incomes. You can then calculate the average variance between the incomes weighted by the number of individuals in each bucket and divide it by 2 X the average income (bucket). In doing so you've created a rough gini coefficient for each zipcode.
You should note that this statistic is rough and not perfectly accurate since it ignores any variation in distribution of income within the bucket. It may be that the 25K-50K bucket has most of its individuals at 40K income and few in the 25K income which would negatively bias your gini estimate.
Assuming this is for a research paper this methodology should be discussed and the possible flaws with this estimate should be disclosed. It does however provide the best approximation for inequality given the information you have.