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

generates a code of length 71 over Z7[X]/(X^2) who´s minimum homogenous weight is 385.

Homogenous weight enumerator: w(x)=1x^0+198x^385+840x^392+1422x^399+1614x^406+1800x^413+2058x^414+1836x^420+24696x^421+2094x^427+74088x^428+1878x^434+1686x^441+1530x^448+924x^455+576x^462+294x^469+84x^476+24x^483+6x^490

The gray image is a linear code over GF(7) with n=497, k=6 and d=385.
This code was found by Heurico 1.16 in 15.9 seconds.