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

generates a code of length 70 over Z7[X]/(X^2) who´s minimum homogenous weight is 399.

Homogenous weight enumerator: w(x)=1x^0+378x^399+438x^406+462x^413+14712x^420+234x^427+174x^434+108x^441+114x^448+54x^455+66x^462+42x^469+12x^476+6x^483+6x^490

The gray image is a linear code over GF(7) with n=490, k=5 and d=399.
This code was found by Heurico 1.16 in 0.396 seconds.