The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1
 0  X  0  0  X  X 4X 2X 3X  0  X 3X 3X  X  0
 0  0  X  0 5X 4X 3X 5X 6X 3X 3X 3X 5X 3X  0
 0  0  0  X 5X  X 2X 6X 6X 4X  X  0 2X 2X  0

generates a code of length 15 over Z7[X]/(X^2) who´s minimum homogenous weight is 70.

Homogenous weight enumerator: w(x)=1x^0+144x^70+354x^77+420x^84+14406x^90+510x^91+714x^98+258x^105

The gray image is a linear code over GF(7) with n=105, k=5 and d=70.
This code was found by Heurico 1.16 in 0.0469 seconds.