The generator matrix

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

generates a code of length 65 over Z7[X]/(X^2) who´s minimum homogenous weight is 378.

Homogenous weight enumerator: w(x)=1x^0+330x^378+252x^379+462x^380+1260x^382+1764x^383+2058x^385+1008x^386+756x^387+1008x^389+588x^390+642x^392+168x^393+336x^394+1848x^396+1764x^397+1380x^399+630x^400+504x^401+30x^406+12x^413+6x^420

The gray image is a linear code over GF(7) with n=455, k=5 and d=378.
This code was found by Heurico 1.16 in 0.147 seconds.