The generator matrix

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

generates a code of length 74 over Z7[X]/(X^2) who´s minimum homogenous weight is 406.

Homogenous weight enumerator: w(x)=1x^0+456x^406+1248x^413+1368x^420+3024x^427+10986x^434+38052x^441+56274x^448+1872x^455+1452x^462+1272x^469+816x^476+522x^483+240x^490+54x^497+12x^504

The gray image is a linear code over GF(7) with n=518, k=6 and d=406.
This code was found by Heurico 1.16 in 16.8 seconds.