The generator matrix

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

generates a code of length 98 over Z7[X]/(X^2) who´s minimum homogenous weight is 569.

Homogenous weight enumerator: w(x)=1x^0+1050x^569+84x^570+630x^571+462x^572+798x^573+2328x^574+3360x^575+8274x^576+798x^577+3108x^578+3108x^579+3486x^580+4254x^581+4410x^582+8862x^583+1008x^584+3654x^585+3612x^586+3192x^587+4122x^588+4830x^589+8484x^590+1134x^591+3486x^592+2772x^593+2898x^594+3312x^595+3360x^596+7476x^597+1092x^598+3528x^599+2394x^600+1974x^601+2724x^602+2562x^603+4956x^604+42x^609+12x^616+12x^623

The gray image is a linear code over GF(7) with n=686, k=6 and d=569.
This code was found by Heurico 1.16 in 7.75 seconds.