The generator matrix

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

generates a code of length 13 over Z7[X]/(X^2) who´s minimum homogenous weight is 70.

Homogenous weight enumerator: w(x)=1x^0+120x^70+108x^77+2058x^78+48x^84+66x^91

The gray image is a linear code over GF(7) with n=91, k=4 and d=70.
This code was found by Heurico 1.16 in 0.00123 seconds.