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

generates a code of length 59 over Z7[X]/(X^2) who´s minimum homogenous weight is 315.

Homogenous weight enumerator: w(x)=1x^0+204x^315+954x^322+1434x^329+2034x^336+7122x^343+33792x^350+65466x^357+2166x^364+1860x^371+1404x^378+786x^385+306x^392+114x^399+6x^406

The gray image is a linear code over GF(7) with n=413, k=6 and d=315.
This code was found by Heurico 1.16 in 12.9 seconds.