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

generates a code of length 66 over Z7[X]/(X^2) who´s minimum homogenous weight is 371.

Homogenous weight enumerator: w(x)=1x^0+84x^371+42x^375+168x^376+2100x^377+456x^378+798x^381+1218x^382+1596x^383+8148x^384+492x^385+2016x^388+2268x^389+2436x^390+15876x^391+390x^392+5922x^395+6048x^396+6132x^397+28014x^398+306x^399+5670x^402+4830x^403+4074x^404+17892x^405+132x^406+174x^413+126x^420+90x^427+60x^434+54x^441+24x^448+12x^455

The gray image is a linear code over GF(7) with n=462, k=6 and d=371.
This code was found by Heurico 1.16 in 5.71 seconds.