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

generates a code of length 98 over Z7[X]/(X^2) who´s minimum homogenous weight is 563.

Homogenous weight enumerator: w(x)=1x^0+420x^563+84x^564+126x^565+252x^566+354x^567+1386x^569+2730x^570+1092x^571+1092x^572+1596x^573+534x^574+3864x^576+6594x^577+1680x^578+2814x^579+2394x^580+534x^581+6132x^583+9240x^584+3738x^585+3150x^586+3654x^587+210x^588+8946x^590+12894x^591+5334x^592+4956x^593+4620x^594+222x^595+7182x^597+8904x^598+2478x^599+2268x^600+1890x^601+144x^602+1302x^604+2436x^605+120x^609+54x^616+48x^623+72x^630+18x^637+24x^644+30x^651+12x^658+6x^665+18x^672

The gray image is a linear code over GF(7) with n=686, k=6 and d=563.
This code was found by Heurico 1.16 in 8.77 seconds.