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

generates a code of length 62 over Z7[X]/(X^2) who´s minimum homogenous weight is 350.

Homogenous weight enumerator: w(x)=1x^0+258x^350+126x^351+294x^352+378x^353+1932x^356+1242x^357+2184x^358+3150x^359+1722x^360+4074x^363+2574x^364+5040x^365+5250x^366+3150x^367+8820x^370+6120x^371+11676x^372+11802x^373+5544x^374+11802x^377+6030x^378+9786x^379+8316x^380+3612x^381+2184x^384+156x^385+132x^392+114x^399+72x^406+42x^413+48x^420+18x^427

The gray image is a linear code over GF(7) with n=434, k=6 and d=350.
This code was found by Heurico 1.16 in 5.29 seconds.