The generator matrix

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

generates a code of length 40 over Z7[X]/(X^2) who´s minimum homogenous weight is 231.

Homogenous weight enumerator: w(x)=1x^0+1314x^231+1890x^232+1764x^233+2058x^238+1512x^239+588x^240+3126x^245+2772x^246+1764x^247+6x^266+12x^273

The gray image is a linear code over GF(7) with n=280, k=5 and d=231.
This code was found by Heurico 1.16 in 58 seconds.