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

generates a code of length 43 over Z7[X]/(X^2) who´s minimum homogenous weight is 238.

Homogenous weight enumerator: w(x)=1x^0+324x^238+492x^245+426x^252+14406x^258+330x^259+246x^266+180x^273+216x^280+114x^287+66x^294+6x^301

The gray image is a linear code over GF(7) with n=301, k=5 and d=238.
This code was found by Heurico 1.16 in 0.195 seconds.