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

generates a code of length 97 over Z7[X]/(X^2) who´s minimum homogenous weight is 560.

Homogenous weight enumerator: w(x)=1x^0+312x^560+564x^567+294x^570+420x^574+3528x^577+300x^581+10584x^584+252x^588+132x^595+66x^602+114x^609+66x^616+30x^623+48x^630+42x^637+12x^644+18x^651+18x^658+6x^665

The gray image is a linear code over GF(7) with n=679, k=5 and d=560.
This code was found by Heurico 1.16 in 0.625 seconds.