The generator matrix

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

generates a code of length 60 over Z7[X]/(X^2) who´s minimum homogenous weight is 346.

Homogenous weight enumerator: w(x)=1x^0+756x^346+5712x^347+5838x^348+2058x^349+30x^350+2142x^353+16002x^354+11256x^355+2856x^356+114x^357+3738x^360+16716x^361+10248x^362+2814x^363+168x^364+3654x^367+19194x^368+11760x^369+2562x^370+30x^371

The gray image is a linear code over GF(7) with n=420, k=6 and d=346.
This code was found by Heurico 1.16 in 14.1 seconds.