The generator matrix

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

generates a code of length 79 over Z7[X]/(X^2) who´s minimum homogenous weight is 458.

Homogenous weight enumerator: w(x)=1x^0+3234x^458+3192x^459+630x^460+588x^461+1776x^462+1176x^463+1512x^464+9618x^465+9072x^466+1848x^467+1596x^468+2520x^469+1764x^470+1890x^471+10458x^472+9912x^473+2646x^474+2100x^475+3420x^476+1764x^477+1386x^478+11382x^479+8988x^480+3108x^481+1890x^482+2832x^483+1470x^484+1386x^485+8526x^486+5880x^487+30x^490+18x^497+24x^504+12x^511

The gray image is a linear code over GF(7) with n=553, k=6 and d=458.
This code was found by Heurico 1.16 in 6.05 seconds.