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

generates a code of length 99 over Z7[X]/(X^2) who´s minimum homogenous weight is 574.

Homogenous weight enumerator: w(x)=1x^0+432x^574+540x^581+456x^588+14406x^594+282x^595+174x^602+138x^609+84x^616+96x^623+60x^630+30x^637+24x^644+18x^651+24x^658+12x^665+12x^672+12x^679+6x^693

The gray image is a linear code over GF(7) with n=693, k=5 and d=574.
This code was found by Heurico 1.16 in 96.8 seconds.