The generator matrix

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

generates a code of length 77 over Z7[X]/(X^2) who´s minimum homogenous weight is 446.

Homogenous weight enumerator: w(x)=1x^0+3108x^446+3192x^447+294x^448+1008x^449+1302x^450+2142x^451+1512x^452+8232x^453+7518x^454+1116x^455+3528x^456+3192x^457+4032x^458+1890x^459+8736x^460+10290x^461+1488x^462+4032x^463+2940x^464+3150x^465+1386x^466+8904x^467+9072x^468+1464x^469+3780x^470+2856x^471+3024x^472+1386x^473+8064x^474+4914x^475+30x^476+36x^483+12x^490+18x^497

The gray image is a linear code over GF(7) with n=539, k=6 and d=446.
This code was found by Heurico 1.16 in 5.83 seconds.