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  1  1  1
 0  X  0  X 3X 3X  0  X 3X 2X 2X 2X  0  X 3X 2X 6X 6X 6X 6X 3X 6X  X  0 2X  X 4X 4X 4X 4X 4X  0 3X 2X 6X 4X  0  X 3X
 0  0  X 5X 3X 2X 4X 2X  X 5X  X 4X 5X 4X  0 2X  0  X 2X 6X 5X 4X 6X 6X 3X 3X 4X 3X  0 6X  X 3X 4X 6X 5X 2X 2X  X  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+42x^224+156x^231+2058x^234+126x^238+6x^259+12x^273

The gray image is a linear code over GF(7) with n=273, k=4 and d=224.
This code was found by Heurico 1.16 in 0.00949 seconds.