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

generates a code of length 57 over Z7[X]/(X^2) who´s minimum homogenous weight is 301.

Homogenous weight enumerator: w(x)=1x^0+114x^301+636x^308+1320x^315+1608x^322+294x^324+1866x^329+5292x^331+1878x^336+31752x^338+2340x^343+63504x^345+2166x^350+1830x^357+1500x^364+978x^371+444x^378+114x^385+12x^392

The gray image is a linear code over GF(7) with n=399, k=6 and d=301.
This code was found by Heurico 1.16 in 12.2 seconds.