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

generates a code of length 53 over Z7[X]/(X^2) who´s minimum homogenous weight is 294.

Homogenous weight enumerator: w(x)=1x^0+96x^294+168x^297+168x^298+672x^300+792x^301+798x^303+3402x^304+1470x^305+2016x^307+3030x^308+2016x^310+7308x^311+2814x^312+3150x^314+10752x^315+5922x^317+17724x^318+5754x^319+5544x^321+15864x^322+5670x^324+14616x^325+4200x^326+3024x^328+216x^329+138x^336+126x^343+120x^350+36x^357+42x^364

The gray image is a linear code over GF(7) with n=371, k=6 and d=294.
This code was found by Heurico 1.16 in 4.49 seconds.