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

generates a code of length 53 over Z7[X]/(X^2) who´s minimum homogenous weight is 304.

Homogenous weight enumerator: w(x)=1x^0+3234x^304+4704x^305+840x^306+126x^307+18x^308+16758x^311+13020x^312+1890x^313+630x^314+138x^315+18522x^318+13944x^319+1638x^320+1302x^321+180x^322+23226x^325+15666x^326+1806x^327+6x^350

The gray image is a linear code over GF(7) with n=371, k=6 and d=304.
This code was found by Heurico 1.16 in 3.65 seconds.