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

generates a code of length 91 over Z7[X]/(X^2) who´s minimum homogenous weight is 520.

Homogenous weight enumerator: w(x)=1x^0+42x^520+126x^522+84x^523+168x^524+456x^525+1344x^526+924x^527+756x^529+1302x^530+1806x^531+474x^532+6174x^533+2226x^534+2184x^536+2436x^537+2100x^538+348x^539+11004x^540+2814x^541+3822x^543+3444x^544+4116x^545+318x^546+21462x^547+3612x^548+4788x^550+4872x^551+4158x^552+216x^553+16128x^554+3486x^555+2730x^557+2268x^558+2058x^559+186x^560+1512x^561+1302x^562+96x^567+84x^574+60x^581+54x^588+18x^595+54x^602+12x^609+24x^616

The gray image is a linear code over GF(7) with n=637, k=6 and d=520.
This code was found by Heurico 1.16 in 21.2 seconds.