The generator matrix

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

generates a code of length 78 over Z7[X]/(X^2) who´s minimum homogenous weight is 452.

Homogenous weight enumerator: w(x)=1x^0+2940x^452+3276x^453+672x^454+1230x^455+1050x^456+1134x^457+1554x^458+8526x^459+8442x^460+2394x^461+3768x^462+2520x^463+1932x^464+1722x^465+10248x^466+8904x^467+3486x^468+3420x^469+2394x^470+1554x^471+1596x^472+9198x^473+8736x^474+3738x^475+4176x^476+2268x^477+1554x^478+1302x^479+8190x^480+5628x^481+24x^483+36x^490+30x^497+6x^504

The gray image is a linear code over GF(7) with n=546, k=6 and d=452.
This code was found by Heurico 1.16 in 6.35 seconds.