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

generates a code of length 68 over Z7[X]/(X^2) who´s minimum homogenous weight is 385.

Homogenous weight enumerator: w(x)=1x^0+180x^385+522x^392+444x^399+2058x^402+372x^406+12348x^409+246x^413+210x^420+96x^427+114x^434+84x^441+24x^448+72x^455+30x^462+6x^469

The gray image is a linear code over GF(7) with n=476, k=5 and d=385.
This code was found by Heurico 1.16 in 0.355 seconds.