The generator matrix

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

generates a code of length 54 over Z7[X]/(X^2) who´s minimum homogenous weight is 315.

Homogenous weight enumerator: w(x)=1x^0+72x^315+1890x^316+3528x^317+1050x^318+108x^322+1512x^323+1176x^324+252x^325+120x^329+2772x^330+3528x^331+756x^332+36x^336+6x^350

The gray image is a linear code over GF(7) with n=378, k=5 and d=315.
This code was found by Heurico 1.16 in 4.75 seconds.