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

generates a code of length 58 over Z7[X]/(X^2) who´s minimum homogenous weight is 308.

Homogenous weight enumerator: w(x)=1x^0+78x^308+762x^315+1476x^322+1596x^329+294x^330+1746x^336+5292x^337+2220x^343+31752x^344+2226x^350+63504x^351+2178x^357+1764x^364+1446x^371+798x^378+414x^385+90x^392+12x^399

The gray image is a linear code over GF(7) with n=406, k=6 and d=308.
This code was found by Heurico 1.16 in 12.5 seconds.