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

generates a code of length 92 over Z7[X]/(X^2) who´s minimum homogenous weight is 532.

Homogenous weight enumerator: w(x)=1x^0+444x^532+528x^539+2526x^546+12612x^553+174x^560+108x^567+96x^574+96x^581+60x^588+54x^595+42x^602+18x^609+30x^616+6x^623+6x^630+6x^637

The gray image is a linear code over GF(7) with n=644, k=5 and d=532.
This code was found by Heurico 1.16 in 76.6 seconds.