The generator matrix

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

generates a code of length 60 over Z7[X]/(X^2) who´s minimum homogenous weight is 349.

Homogenous weight enumerator: w(x)=1x^0+882x^349+78x^350+840x^351+588x^352+1764x^353+2646x^356+126x^357+1260x^358+588x^359+588x^360+882x^363+72x^364+2016x^365+882x^366+1764x^367+1764x^370+18x^371+24x^378+24x^385

The gray image is a linear code over GF(7) with n=420, k=5 and d=349.
This code was found by Heurico 1.16 in 0.127 seconds.