The generator matrix

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

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+42x^493+42x^494+336x^495+1512x^496+870x^497+1344x^500+630x^501+3360x^502+5628x^503+2040x^504+2604x^507+2268x^508+4746x^509+8106x^510+3696x^511+3108x^514+5754x^515+9576x^516+13230x^517+5688x^518+5082x^521+5712x^522+9114x^523+11760x^524+3828x^525+2226x^528+1680x^530+2982x^531+186x^532+108x^539+84x^546+72x^553+42x^560+18x^567+30x^574+24x^581+6x^588

The gray image is a linear code over GF(7) with n=602, k=6 and d=490.
This code was found by Heurico 1.16 in 7.71 seconds.