014 Balanced Trincubic
At first glance, it seems very confusing, but it does make the overall system much easier to use. Addition, multiplication, rounding... A person just has to get used to using negative ternary sub-digits.
Unbalanced Trincubic can be converted to Balanced Trincubic by adding ternary sub digits 1111.. with carry, then subtracting 1111... without borrow (the string of 1s must be the same length, so if the result of the addition has more sub digits, subtract nothing from these extra sub digits). For example, 0213 + 1113 = 2023, 2023 − 1113 = 1113(bal) = 710.