The generator matrix

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

generates a code of length 77 over Z7[X]/(X^2) who´s minimum homogenous weight is 440.

Homogenous weight enumerator: w(x)=1x^0+882x^440+384x^441+168x^442+882x^443+7014x^447+468x^448+1512x^449+3192x^450+12684x^454+432x^455+2688x^456+6300x^457+19530x^461+372x^462+5880x^463+11340x^464+24192x^468+192x^469+4158x^470+7098x^471+7728x^475+108x^476+120x^483+84x^490+90x^497+60x^504+60x^511+18x^518+12x^525

The gray image is a linear code over GF(7) with n=539, k=6 and d=440.
This code was found by Heurico 1.16 in 91.3 seconds.