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

generates a code of length 93 over Z7[X]/(X^2) who´s minimum homogenous weight is 532.

Homogenous weight enumerator: w(x)=1x^0+114x^532+438x^539+804x^546+3906x^553+10800x^560+204x^567+156x^574+102x^581+66x^588+48x^595+78x^602+30x^609+18x^616+18x^623+12x^630+12x^637

The gray image is a linear code over GF(7) with n=651, k=5 and d=532.
This code was found by Heurico 1.16 in 0.579 seconds.