The generator matrix

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

generates a code of length 98 over Z7[X]/(X^2) who´s minimum homogenous weight is 577.

Homogenous weight enumerator: w(x)=1x^0+294x^577+1806x^579+3024x^580+114x^581+882x^584+2268x^586+3024x^587+126x^588+294x^591+630x^593+168x^594+36x^595+588x^598+1470x^600+2016x^601+48x^602+6x^609+12x^616

The gray image is a linear code over GF(7) with n=686, k=5 and d=577.
This code was found by Heurico 1.16 in 26 seconds.