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

generates a code of length 99 over Z7[X]/(X^2) who´s minimum homogenous weight is 567.

Homogenous weight enumerator: w(x)=1x^0+120x^567+84x^569+210x^570+756x^573+1764x^574+462x^575+1134x^576+1680x^577+3738x^580+4266x^581+1470x^582+2562x^583+4200x^584+5418x^587+6618x^588+3402x^589+2898x^590+7560x^591+7266x^594+6780x^595+5460x^596+3318x^597+9786x^598+8106x^601+8196x^602+3612x^603+3234x^604+5376x^605+3528x^608+3018x^609+1176x^611+126x^616+84x^623+60x^630+72x^637+42x^644+30x^651+24x^658+12x^665

The gray image is a linear code over GF(7) with n=693, k=6 and d=567.
This code was found by Heurico 1.16 in 9.28 seconds.