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

generates a code of length 68 over Z16 who´s minimum homogenous weight is 64.

Homogenous weight enumerator: w(x)=1x^0+282x^64+1504x^68+248x^72+12x^80+1x^128

The gray image is a code over GF(2) with n=544, k=11 and d=256.
This code was found by Heurico 1.16 in 15.3 seconds.