The generator matrix

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

generates a code of length 87 over Z7[X]/(X^2) who´s minimum homogenous weight is 511.

Homogenous weight enumerator: w(x)=1x^0+1170x^511+924x^512+588x^513+756x^514+3822x^518+1512x^519+798x^520+756x^521+1098x^525+672x^526+168x^527+42x^528+2430x^532+1008x^533+504x^534+504x^535+36x^539+12x^546+6x^553

The gray image is a linear code over GF(7) with n=609, k=5 and d=511.
This code was found by Heurico 1.16 in 0.251 seconds.