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

generates a code of length 86 over Z7[X]/(X^2) who´s minimum homogenous weight is 509.

Homogenous weight enumerator: w(x)=1x^0+882x^509+174x^511+294x^516+102x^518+882x^523+36x^525+6x^532+6x^539+6x^546+12x^553

The gray image is a linear code over GF(7) with n=602, k=4 and d=509.
This code was found by Heurico 1.16 in 0.364 seconds.