The generator matrix

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

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+210x^350+570x^357+294x^360+426x^364+3528x^367+342x^371+10584x^374+222x^378+174x^385+144x^392+150x^399+66x^406+36x^413+42x^420+12x^427+6x^434

The gray image is a linear code over GF(7) with n=434, k=5 and d=350.
This code was found by Heurico 1.16 in 0.312 seconds.