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

generates a code of length 87 over Z7[X]/(X^2) who´s minimum homogenous weight is 497.

Homogenous weight enumerator: w(x)=1x^0+360x^497+672x^502+1260x^503+2442x^504+1050x^505+798x^507+2016x^509+4368x^510+6510x^511+2268x^512+2016x^514+2730x^516+5460x^517+9852x^518+3066x^519+5922x^521+3864x^523+9198x^524+15978x^525+5502x^526+5670x^528+3528x^530+7308x^531+9978x^532+2520x^533+1596x^537+1218x^538+114x^539+84x^546+108x^553+48x^560+60x^567+36x^574+18x^581+24x^588+6x^595

The gray image is a linear code over GF(7) with n=609, k=6 and d=497.
This code was found by Heurico 1.16 in 7.83 seconds.