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

generates a code of length 61 over Z7[X]/(X^2) who´s minimum homogenous weight is 329.

Homogenous weight enumerator: w(x)=1x^0+354x^329+1212x^336+1428x^343+294x^348+1818x^350+5292x^355+1914x^357+31752x^362+2076x^364+63504x^369+2154x^371+2022x^378+1626x^385+1206x^392+642x^399+294x^406+48x^413+12x^420

The gray image is a linear code over GF(7) with n=427, k=6 and d=329.
This code was found by Heurico 1.16 in 13.7 seconds.