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

generates a code of length 89 over Z7[X]/(X^2) who´s minimum homogenous weight is 525.

Homogenous weight enumerator: w(x)=1x^0+5238x^525+5418x^532+2232x^539+3906x^546+12x^574

The gray image is a linear code over GF(7) with n=623, k=5 and d=525.
This code was found by Heurico 1.16 in 5.62 seconds.