The generator matrix

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

generates a code of length 77 over Z7[X]/(X^2) who´s minimum homogenous weight is 452.

Homogenous weight enumerator: w(x)=1x^0+1302x^452+1218x^453+630x^454+1878x^455+2520x^459+1470x^460+504x^461+750x^462+756x^466+462x^467+924x^468+1782x^469+1596x^473+966x^474+12x^476+12x^483+18x^490+6x^497

The gray image is a linear code over GF(7) with n=539, k=5 and d=452.
This code was found by Heurico 1.16 in 5.91 seconds.