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

generates a code of length 58 over Z7[X]/(X^2) who´s minimum homogenous weight is 329.

Homogenous weight enumerator: w(x)=1x^0+480x^329+432x^336+444x^343+14406x^348+342x^350+156x^357+144x^364+150x^371+126x^378+72x^385+36x^392+6x^399+12x^406

The gray image is a linear code over GF(7) with n=406, k=5 and d=329.
This code was found by Heurico 1.16 in 60 seconds.