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

generates a code of length 61 over Z7[X]/(X^2) who´s minimum homogenous weight is 343.

Homogenous weight enumerator: w(x)=1x^0+564x^343+42x^345+2226x^349+2688x^350+798x^351+1176x^352+5712x^356+5850x^357+2016x^358+2394x^359+11844x^363+15018x^364+5922x^365+5922x^366+18186x^370+18192x^371+5670x^372+4872x^373+5250x^377+2820x^378+150x^385+156x^392+60x^399+66x^406+30x^413+24x^420

The gray image is a linear code over GF(7) with n=427, k=6 and d=343.
This code was found by Heurico 1.16 in 5.24 seconds.