The generator matrix

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

generates a code of length 90 over Z7[X]/(X^2) who´s minimum homogenous weight is 518.

Homogenous weight enumerator: w(x)=1x^0+822x^518+462x^519+126x^520+210x^521+2982x^523+3450x^525+1722x^526+1638x^527+2352x^528+6972x^530+5916x^532+2856x^533+2562x^534+2268x^535+9702x^537+7410x^539+3234x^540+5922x^541+6090x^542+15666x^544+8838x^546+4578x^547+4158x^548+3486x^549+7896x^551+4326x^553+1554x^554+132x^560+60x^567+78x^574+66x^581+42x^588+48x^595+12x^602+12x^609

The gray image is a linear code over GF(7) with n=630, k=6 and d=518.
This code was found by Heurico 1.16 in 62.2 seconds.