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

generates a code of length 66 over Z7[X]/(X^2) who´s minimum homogenous weight is 357.

Homogenous weight enumerator: w(x)=1x^0+228x^357+1128x^364+1296x^371+1866x^378+2058x^384+1938x^385+24696x^391+1806x^392+74088x^398+1878x^399+2022x^406+1890x^413+1272x^420+882x^427+444x^434+132x^441+24x^448

The gray image is a linear code over GF(7) with n=462, k=6 and d=357.
This code was found by Heurico 1.16 in 14.7 seconds.