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

generates a code of length 60 over Z7[X]/(X^2) who´s minimum homogenous weight is 322.

Homogenous weight enumerator: w(x)=1x^0+222x^322+1044x^329+1602x^336+1638x^343+1944x^350+1974x^357+100842x^360+2232x^364+2010x^371+1788x^378+1194x^385+834x^392+276x^399+42x^406+6x^420

The gray image is a linear code over GF(7) with n=420, k=6 and d=322.
This code was found by Heurico 1.16 in 13.5 seconds.