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

generates a code of length 66 over Z7[X]/(X^2) who´s minimum homogenous weight is 371.

Homogenous weight enumerator: w(x)=1x^0+90x^371+450x^378+294x^384+516x^385+3528x^391+348x^392+10584x^398+258x^399+240x^406+132x^413+138x^420+72x^427+84x^434+36x^441+18x^448+12x^455+6x^462

The gray image is a linear code over GF(7) with n=462, k=5 and d=371.
This code was found by Heurico 1.16 in 0.339 seconds.