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

generates a code of length 54 over Z7[X]/(X^2) who´s minimum homogenous weight is 301.

Homogenous weight enumerator: w(x)=1x^0+120x^301+84x^303+504x^304+1332x^308+798x^309+2394x^310+4536x^311+3948x^315+2016x^316+4662x^317+8064x^318+11598x^322+5922x^323+11970x^324+17640x^325+13560x^329+5670x^330+9702x^331+12474x^332+210x^336+108x^343+144x^350+120x^357+54x^364+12x^371+6x^378

The gray image is a linear code over GF(7) with n=378, k=6 and d=301.
This code was found by Heurico 1.16 in 4.6 seconds.