The generator matrix

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

generates a code of length 48 over Z7[X]/(X^2) who´s minimum homogenous weight is 266.

Homogenous weight enumerator: w(x)=1x^0+174x^266+540x^273+456x^280+300x^287+14406x^288+282x^294+174x^301+210x^308+168x^315+72x^322+18x^329+6x^336

The gray image is a linear code over GF(7) with n=336, k=5 and d=266.
This code was found by Heurico 1.16 in 0.225 seconds.