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

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+456x^231+480x^238+372x^245+14406x^246+288x^252+174x^259+234x^266+120x^273+84x^280+12x^287

The gray image is a linear code over GF(7) with n=287, k=5 and d=224.
This code was found by Heurico 1.16 in 0.186 seconds.