The generator matrix

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

generates a code of length 70 over Z7[X]/(X^2) who´s minimum homogenous weight is 416.

Homogenous weight enumerator: w(x)=1x^0+630x^416+252x^419+618x^420+840x^423+42x^426+12x^441+6x^448

The gray image is a linear code over GF(7) with n=490, k=4 and d=416.
This code was found by Heurico 1.16 in 15.3 seconds.