The generator matrix

 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  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  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  X
 0  X  0  0  X  X 4X 2X 3X  0  X 3X 3X 3X 5X 2X 2X  X 4X 2X 3X 4X  0  0 4X  X  X 3X  0 4X 6X 4X  0 6X 4X 3X 3X 6X  X 2X 2X 3X  0 4X 5X 5X  X 5X 3X  0  X 2X  0  X 2X 3X 4X 2X 2X 4X 6X 5X 5X  0 3X 5X 5X  X 3X  X 6X 2X 4X  X 4X 2X 2X  X 6X 6X 2X 2X 6X 6X 2X 5X 5X 4X  X 3X 3X 6X 4X 6X 2X 6X  X  X
 0  0  X  0 5X 4X 3X 5X 6X 3X 3X 3X 5X 5X 4X  0  0 3X  X 4X 2X  X  X 5X  0  X  X  X 5X  0 5X 2X 4X 4X 3X 4X 2X  X 4X  X 4X 3X  0 2X 2X 3X  0  0 3X 4X 5X 5X 5X 3X 6X 2X  0  X 4X 5X 5X 6X  0 6X  X 4X 2X 6X 4X 5X 3X 2X 4X  X 4X  0 5X 6X 6X 6X  X  0  0 6X 4X  X 3X 3X  X 5X  X  0  X 3X 2X 3X 2X 2X
 0  0  0  X 5X  X 2X 6X 6X 4X  X  0 2X 6X 6X 5X  X 2X 5X  X  X 3X 2X 4X 5X 5X 2X  0 5X 4X 2X 4X 3X 6X  X 3X 2X 6X 2X 6X 5X 3X 2X 3X  X 3X 4X 5X 5X 6X 6X 3X 3X 3X 3X 6X 6X 4X 4X 3X  0 4X  0  X 3X 4X 5X 6X 5X 2X  X 5X 4X 4X 5X 6X 4X 4X 3X  X 5X 4X 3X 4X  0 2X 2X 5X 3X 3X 2X 4X 6X 5X 3X 2X 4X 5X

generates a code of length 98 over Z7[X]/(X^2) who´s minimum homogenous weight is 567.

Homogenous weight enumerator: w(x)=1x^0+408x^567+504x^574+294x^576+450x^581+3528x^583+300x^588+10584x^590+180x^595+156x^602+66x^609+96x^616+60x^623+42x^630+60x^637+18x^644+36x^651+18x^658+6x^672

The gray image is a linear code over GF(7) with n=686, k=5 and d=567.
This code was found by Heurico 1.16 in 5.36 seconds.