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

generates a code of length 44 over Z7[X]/(X^2) who´s minimum homogenous weight is 245.

Homogenous weight enumerator: w(x)=1x^0+384x^245+492x^252+408x^259+14406x^264+318x^266+294x^273+138x^280+186x^287+144x^294+24x^301+12x^308

The gray image is a linear code over GF(7) with n=308, k=5 and d=245.
This code was found by Heurico 1.16 in 0.212 seconds.