The generator matrix

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

generates a code of length 70 over Z7[X]/(X^2) who´s minimum homogenous weight is 403.

Homogenous weight enumerator: w(x)=1x^0+1386x^403+1890x^404+420x^405+156x^406+630x^407+1806x^408+3276x^409+7602x^410+6048x^411+3234x^412+738x^413+1680x^414+2436x^415+5922x^416+10080x^417+7686x^418+4620x^419+600x^420+1806x^421+2940x^422+4788x^423+9702x^424+8316x^425+6132x^426+828x^427+2058x^428+3108x^429+4536x^430+8274x^431+4872x^432+18x^434+6x^441+42x^448+12x^455

The gray image is a linear code over GF(7) with n=490, k=6 and d=403.
This code was found by Heurico 1.16 in 5.23 seconds.