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

generates a code of length 40 over Z7[X]/(X^2) who´s minimum homogenous weight is 217.

Homogenous weight enumerator: w(x)=1x^0+138x^217+444x^224+294x^228+426x^231+3528x^235+426x^238+10584x^242+282x^245+234x^252+216x^259+126x^266+102x^273+6x^280

The gray image is a linear code over GF(7) with n=280, k=5 and d=217.
This code was found by Heurico 1.16 in 0.181 seconds.