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

generates a code of length 65 over Z7[X]/(X^2) who´s minimum homogenous weight is 373.

Homogenous weight enumerator: w(x)=1x^0+1680x^373+168x^374+42x^375+714x^376+1218x^377+3306x^378+3486x^379+8190x^380+1008x^381+1092x^382+2352x^383+4368x^384+6858x^385+5334x^386+11256x^387+1890x^388+1218x^389+3444x^390+4074x^391+5988x^392+5334x^393+10878x^394+3108x^395+1764x^396+3780x^397+4746x^398+6762x^399+4368x^400+9156x^401+30x^406+12x^413+18x^420+6x^427

The gray image is a linear code over GF(7) with n=455, k=6 and d=373.
This code was found by Heurico 1.16 in 4.77 seconds.