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

generates a code of length 85 over Z7[X]/(X^2) who´s minimum homogenous weight is 490.

Homogenous weight enumerator: w(x)=1x^0+432x^490+516x^497+294x^498+426x^504+3528x^505+342x^511+10584x^512+168x^518+132x^525+90x^532+84x^539+48x^546+54x^553+42x^560+24x^567+24x^574+18x^581

The gray image is a linear code over GF(7) with n=595, k=5 and d=490.
This code was found by Heurico 1.16 in 92.7 seconds.