The generator matrix

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

generates a code of length 44 over Z7[X]/(X^2) who´s minimum homogenous weight is 255.

Homogenous weight enumerator: w(x)=1x^0+1680x^255+2520x^256+138x^259+2520x^262+2016x^263+168x^266+4032x^269+3696x^270+24x^273+6x^287+6x^308

The gray image is a linear code over GF(7) with n=308, k=5 and d=255.
This code was found by Heurico 1.16 in 0.369 seconds.