The generator matrix

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

generates a code of length 53 over Z7[X]/(X^2) who´s minimum homogenous weight is 308.

Homogenous weight enumerator: w(x)=1x^0+60x^308+2520x^310+2646x^311+1050x^312+108x^315+2016x^317+882x^318+252x^319+114x^322+3696x^324+2646x^325+756x^326+48x^329+6x^336+6x^343

The gray image is a linear code over GF(7) with n=371, k=5 and d=308.
This code was found by Heurico 1.16 in 23.9 seconds.