The generator matrix

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

generates a code of length 39 over Z7[X]/(X^2) who´s minimum homogenous weight is 224.

Homogenous weight enumerator: w(x)=1x^0+798x^224+1260x^225+1218x^226+2184x^231+1890x^232+1092x^233+3498x^238+3024x^239+1806x^240+18x^245+6x^252+12x^273

The gray image is a linear code over GF(7) with n=273, k=5 and d=224.
This code was found by Heurico 1.16 in 0.0678 seconds.