The generator matrix

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

generates a code of length 86 over Z7[X]/(X^2) who´s minimum homogenous weight is 500.

Homogenous weight enumerator: w(x)=1x^0+3024x^500+4032x^501+1806x^502+420x^503+666x^504+1890x^505+1008x^506+10626x^507+8652x^508+2772x^509+1092x^510+1158x^511+3360x^512+1344x^513+11088x^514+8946x^515+3024x^516+1260x^517+1434x^518+2310x^519+756x^520+11466x^521+8820x^522+3108x^523+1344x^524+1146x^525+2730x^526+1008x^527+9072x^528+6594x^529+1638x^530+30x^532+12x^539+12x^546

The gray image is a linear code over GF(7) with n=602, k=6 and d=500.
This code was found by Heurico 1.16 in 6.31 seconds.