The generator matrix

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

generates a code of length 70 over Z7[X]/(X^2) who´s minimum homogenous weight is 398.

Homogenous weight enumerator: w(x)=1x^0+630x^398+420x^399+168x^400+840x^404+5544x^405+1578x^406+1470x^407+3360x^411+10038x^412+2904x^413+2814x^414+11340x^418+15876x^419+6282x^420+5754x^421+13272x^425+19824x^426+5034x^427+4200x^428+5712x^433+168x^434+108x^441+84x^448+114x^455+54x^462+36x^469+18x^476+6x^490

The gray image is a linear code over GF(7) with n=490, k=6 and d=398.
This code was found by Heurico 1.16 in 18 seconds.