The generator matrix

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

generates a code of length 70 over Z7[X]/(X^2) who´s minimum homogenous weight is 413.

Homogenous weight enumerator: w(x)=1x^0+150x^413+294x^414+114x^420+1764x^421+18x^427+24x^434+30x^441+6x^483

The gray image is a linear code over GF(7) with n=490, k=4 and d=413.
This code was found by Heurico 1.16 in 0.0503 seconds.