The board of supervisors shall have the right and power to keep and maintain any such levee, ditches, drains, or system of drainage, either in whole or in part, established under sections 468.390 through 468.395, as may in their judgment be required, and to levy the expense thereof upon the real estate within such drainage district as provided for in this part, and collect and expend the same; provided, however, that no such work which shall impose a tax exceeding three dollars and thirty-seven and one-half cents per thousand dollars on the assessable value of the lands and improvements within the district shall be authorized by the board, unless the work is first petitioned for and authorized in substantially the manner required by this part for the inauguration of new work. However, if such work is of the kinds contemplated by section 468.126, and the cost thereof is within the limitations of section 468.126, or is of the kinds contemplated by section 468.188, and the cost thereof is within the limitations of section 468.188, then the provisions of section 468.126 or section 468.188 shall supersede the limitations of this section.