The generator matrix

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

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+1488x^245+84x^246+168x^247+420x^248+6258x^252+1512x^253+1260x^254+1680x^255+12714x^259+9072x^260+5208x^261+5670x^262+28068x^266+18144x^267+7770x^268+6636x^269+10950x^273+222x^280+168x^287+108x^294+36x^301+12x^308

The gray image is a linear code over GF(7) with n=308, k=6 and d=245.
This code was found by Heurico 1.16 in 69.9 seconds.