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

generates a code of length 86 over Z7[X]/(X^2) who´s minimum homogenous weight is 490.

Homogenous weight enumerator: w(x)=1x^0+114x^490+468x^497+708x^504+3918x^511+10866x^518+216x^525+150x^532+66x^539+78x^546+78x^553+54x^560+36x^567+24x^574+18x^581+12x^588

The gray image is a linear code over GF(7) with n=602, k=5 and d=490.
This code was found by Heurico 1.16 in 0.512 seconds.