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

generates a code of length 83 over Z7[X]/(X^2) who´s minimum homogenous weight is 455.

Homogenous weight enumerator: w(x)=1x^0+126x^455+822x^462+1398x^469+42x^474+1626x^476+1008x^481+1842x^483+9072x^488+1860x^490+36288x^495+1818x^497+54432x^502+1518x^504+1614x^511+1356x^518+1086x^525+786x^532+564x^539+264x^546+102x^553+24x^560

The gray image is a linear code over GF(7) with n=581, k=6 and d=455.
This code was found by Heurico 1.16 in 19.6 seconds.