The generator matrix

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

generates a code of length 65 over Z7[X]/(X^2) who´s minimum homogenous weight is 364.

Homogenous weight enumerator: w(x)=1x^0+102x^364+252x^366+126x^369+546x^370+906x^371+1134x^373+3654x^376+4326x^377+1938x^378+1806x^380+6804x^383+8442x^384+3402x^385+3192x^387+18144x^390+17346x^391+6282x^392+5040x^394+14490x^397+12558x^398+3648x^399+2982x^401+156x^406+108x^413+96x^420+96x^427+30x^434+12x^441+24x^448+6x^455

The gray image is a linear code over GF(7) with n=455, k=6 and d=364.
This code was found by Heurico 1.16 in 5.6 seconds.