The generator matrix

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

generates a code of length 16 over Z7[X]/(X^2) who´s minimum homogenous weight is 84.

Homogenous weight enumerator: w(x)=1x^0+660x^84+3150x^85+1260x^86+882x^90+7710x^91+15750x^92+3360x^93+18522x^96+5292x^97+22770x^98+32550x^99+5670x^100+18x^105+54x^112

The gray image is a linear code over GF(7) with n=112, k=6 and d=84.
This code was found by Heurico 1.16 in 0.759 seconds.