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

generates a code of length 88 over Z7[X]/(X^2) who´s minimum homogenous weight is 518.

Homogenous weight enumerator: w(x)=1x^0+2010x^518+630x^519+2394x^520+2988x^525+714x^526+2016x^527+1446x^532+210x^533+252x^534+2106x^539+504x^540+1512x^541+6x^546+6x^553+12x^560

The gray image is a linear code over GF(7) with n=616, k=5 and d=518.
This code was found by Heurico 1.16 in 22.3 seconds.