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.