The generator matrix

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

generates a code of length 60 over Z7[X]/(X^2) who´s minimum homogenous weight is 336.

Homogenous weight enumerator: w(x)=1x^0+114x^336+42x^339+126x^340+336x^341+1218x^342+474x^343+840x^344+756x^345+1176x^346+1554x^347+1890x^348+4410x^349+510x^350+3360x^351+2142x^352+2394x^353+2814x^354+2898x^355+5922x^356+360x^357+11340x^358+5796x^359+5922x^360+5670x^361+5712x^362+11214x^363+240x^364+13272x^365+5712x^366+4872x^367+4242x^368+3570x^369+6048x^370+216x^371+150x^378+102x^385+114x^392+66x^399+48x^406+6x^413

The gray image is a linear code over GF(7) with n=420, k=6 and d=336.
This code was found by Heurico 1.16 in 5.15 seconds.