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

generates a code of length 94 over Z7[X]/(X^2) who´s minimum homogenous weight is 551.

Homogenous weight enumerator: w(x)=1x^0+504x^551+168x^552+48x^553+588x^555+756x^556+882x^557+3612x^558+924x^559+138x^560+798x^562+756x^563+294x^564+1722x^565+294x^566+72x^567+168x^569+42x^570+882x^571+1344x^572+672x^573+54x^574+504x^576+504x^577+1050x^579+12x^581+6x^595+6x^602+6x^609

The gray image is a linear code over GF(7) with n=658, k=5 and d=551.
This code was found by Heurico 1.16 in 0.3 seconds.