The generator matrix

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

generates a code of length 41 over Z7[X]/(X^2) who´s minimum homogenous weight is 224.

Homogenous weight enumerator: w(x)=1x^0+180x^224+126x^225+42x^228+126x^229+1176x^230+2046x^231+840x^232+756x^235+1386x^236+5292x^237+4530x^238+2898x^239+4536x^242+5082x^243+16758x^244+12078x^245+5586x^246+9072x^249+7812x^250+19992x^251+11754x^252+4956x^253+240x^259+210x^266+102x^273+48x^280+24x^287

The gray image is a linear code over GF(7) with n=287, k=6 and d=224.
This code was found by Heurico 1.16 in 3.29 seconds.