The generator matrix

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

generates a code of length 97 over Z7[X]/(X^2) who´s minimum homogenous weight is 573.

Homogenous weight enumerator: w(x)=1x^0+4242x^573+816x^574+5208x^580+942x^581+1554x^587+84x^588+3402x^594+546x^595+6x^616+6x^623

The gray image is a linear code over GF(7) with n=679, k=5 and d=573.
This code was found by Heurico 1.16 in 0.317 seconds.