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

generates a code of length 38 over Z7[X]/(X^2) who´s minimum homogenous weight is 210.

Homogenous weight enumerator: w(x)=1x^0+414x^210+168x^211+498x^217+1260x^218+366x^224+5208x^225+384x^231+7770x^232+270x^238+198x^245+150x^252+108x^259+12x^266

The gray image is a linear code over GF(7) with n=266, k=5 and d=210.
This code was found by Heurico 1.16 in 0.883 seconds.