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

generates a code of length 67 over Z7[X]/(X^2) who´s minimum homogenous weight is 364.

Homogenous weight enumerator: w(x)=1x^0+288x^364+1164x^371+1698x^378+2700x^385+10896x^392+38244x^399+56478x^406+1902x^413+1596x^420+1296x^427+780x^434+468x^441+102x^448+36x^455

The gray image is a linear code over GF(7) with n=469, k=6 and d=364.
This code was found by Heurico 1.16 in 15 seconds.