The generator matrix

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

generates a code of length 16 over Z7[X]/(X^2) who´s minimum homogenous weight is 77.

Homogenous weight enumerator: w(x)=1x^0+126x^77+168x^79+1908x^84+1260x^86+4116x^90+18072x^91+5208x^93+24696x^97+53496x^98+7770x^100+642x^105+186x^112

The gray image is a linear code over GF(7) with n=112, k=6 and d=77.
This code was found by Heurico 1.16 in 0.986 seconds.