The generator matrix

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

generates a code of length 39 over Z7[X]/(X^2) who´s minimum homogenous weight is 220.

Homogenous weight enumerator: w(x)=1x^0+2982x^220+84x^222+882x^223+390x^224+9114x^225+1134x^226+11466x^227+1008x^229+4410x^230+684x^231+14112x^232+1260x^233+15456x^234+3024x^236+9114x^237+1266x^238+22050x^239+1722x^240+17430x^241+6x^245+42x^252+12x^259

The gray image is a linear code over GF(7) with n=273, k=6 and d=220.
This code was found by Heurico 1.16 in 72.4 seconds.