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

generates a code of length 44 over Z7[X]/(X^2) who´s minimum homogenous weight is 231.

Homogenous weight enumerator: w(x)=1x^0+384x^231+1290x^238+1734x^245+4056x^252+26796x^259+76662x^266+2532x^273+2232x^280+1368x^287+468x^294+114x^301+12x^308

The gray image is a linear code over GF(7) with n=308, k=6 and d=231.
This code was found by Heurico 1.16 in 9.33 seconds.