The generator matrix

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

generates a code of length 89 over Z7[X]/(X^2) who´s minimum homogenous weight is 518.

Homogenous weight enumerator: w(x)=1x^0+3030x^518+4158x^519+3276x^520+546x^521+630x^522+420x^523+9936x^525+8778x^526+5040x^527+2226x^528+1050x^529+546x^530+11454x^532+10374x^533+6090x^534+1176x^535+1302x^536+588x^537+9828x^539+8904x^540+4872x^541+2016x^542+1134x^543+504x^544+9282x^546+6888x^547+3360x^548+210x^549+6x^553+12x^560+12x^567

The gray image is a linear code over GF(7) with n=623, k=6 and d=518.
This code was found by Heurico 1.16 in 6.58 seconds.