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

generates a code of length 92 over Z7[X]/(X^2) who´s minimum homogenous weight is 543.

Homogenous weight enumerator: w(x)=1x^0+3234x^543+2394x^544+126x^546+3318x^550+2016x^551+126x^553+1302x^557+252x^558+66x^560+2436x^564+1512x^565+6x^567+6x^574+12x^588

The gray image is a linear code over GF(7) with n=644, k=5 and d=543.
This code was found by Heurico 1.16 in 44 seconds.