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  2  1  2  2  2  2  2  1  1  1  1  1  1  1  1  2  2  2  2  4  0  2  2  2  2  4  0  4  4  4  4  8  8  4  2  2  1  1  1  1  4  1  1  1  1
 0 12  0 12  8  4  8  4  0 12  0 12  8  4  8  4  0 12  0 12  8  4  8 12  4 12  4  4  0  8  0 12  8  4  0 12  8  4 12 12  0  8 12  4  4  4  0  8 12  4  0  8  4  4  4  4  8  0  8  0  0  8  8  0 12  4 12  4
 0  0  8  8  8  8  0  0  0  0  8  8  8  8  0  0  0  0  8  8  8  8  0  0  0  8  8  0  8  8  0  0  0  0  8  8  8  8  0  8  0  0  0  8  8  0  8  8  8  0  8  8  8  0  8  0  0  0  0  0  8  8  0  0  0  0  8  8

generates a code of length 68 over Z16 who´s minimum homogenous weight is 68.

Homogenous weight enumerator: w(x)=1x^0+112x^68+14x^72+1x^80

The gray image is a code over GF(2) with n=544, k=7 and d=272.
This code was found by Heurico 1.16 in 0.261 seconds.