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

generates a code of length 67 over Z7[X]/(X^2) who´s minimum homogenous weight is 385.

Homogenous weight enumerator: w(x)=1x^0+1758x^385+966x^386+168x^387+756x^388+294x^389+1386x^390+3780x^391+8388x^392+4200x^393+2478x^394+3570x^395+1344x^396+3192x^397+6132x^398+9762x^399+4200x^400+3360x^401+4998x^402+1134x^403+2688x^404+5796x^405+10362x^406+6888x^407+4284x^408+5082x^409+1344x^410+3024x^411+4872x^412+9084x^413+2268x^414+42x^420+30x^427+18x^434

The gray image is a linear code over GF(7) with n=469, k=6 and d=385.
This code was found by Heurico 1.16 in 4.98 seconds.