The generator matrix

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

generates a code of length 66 over Z7[X]/(X^2) who´s minimum homogenous weight is 379.

Homogenous weight enumerator: w(x)=1x^0+1680x^379+42x^381+672x^382+2478x^383+1974x^384+4602x^385+7182x^386+840x^387+504x^388+1974x^389+8736x^390+3276x^391+7968x^392+10290x^393+1260x^394+630x^395+2268x^396+8022x^397+3402x^398+6042x^399+9366x^400+2016x^401+882x^402+3318x^403+9576x^404+3696x^405+6384x^406+8526x^407+24x^413+6x^420+12x^427

The gray image is a linear code over GF(7) with n=462, k=6 and d=379.
This code was found by Heurico 1.16 in 4.96 seconds.