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

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+138x^343+534x^350+486x^357+2058x^360+372x^364+12348x^367+228x^371+162x^378+156x^385+114x^392+114x^399+36x^406+42x^413+12x^420+6x^427

The gray image is a linear code over GF(7) with n=427, k=5 and d=343.
This code was found by Heurico 1.16 in 0.306 seconds.