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  2  2  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  2  2  2  2
 0  8  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  8  0  8  0  8  0  8  0  8  8  8  0  8  0  8  8  8  8  8  8  8  8  8  8  8  0  0  0  8  8  0  0  8  0  8  8  8  8  0  0  8  0  8  8  8  8  8  8  0  0  0  0  0
 0  0  8  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  8  0  8  0  8  0  8  0  8  0  8  8  8  0  8  0  8  8  8  8  8  8  8  8  8  8  0  8  8  0  0  8  8  0  8  8  8  0  0  8  8  8  8  0  8  0  0  8  8  0  0  0  8  8
 0  0  0  8  0  0  0  0  0  0  0  8  8  8  8  8  8  8  8  8  8  8  0  0  8  8  8  8  0  0  0  0  0  0  0  0  0  0  0  0  8  8  8  8  0  8  8  0  0  8  0  8  0  8  8  8  0  8  0  0  0  8  0  8  0  8  8  0  0  8  8  0
 0  0  0  0  8  0  0  0  8  8  8  8  8  0  8  8  0  0  0  0  0  0  0  0  0  0  0  0  8  8  8  8  8  8  0  8  0  8  0  8  8  0  8  0  8  8  8  8  0  8  8  8  0  8  0  8  8  8  0  0  8  8  8  8  0  8  0  0  8  8  0  8
 0  0  0  0  0  8  0  8  8  8  0  0  0  0  8  8  8  8  0  0  0  0  0  0  8  8  8  8  8  8  0  0  0  0  0  8  0  8  8  0  0  8  8  0  8  8  0  8  8  8  8  0  8  8  0  8  8  0  8  8  8  8  0  0  8  0  8  8  0  0  0  0
 0  0  0  0  0  0  8  8  0  8  8  0  8  8  8  0  0  8  0  0  8  8  8  8  8  8  0  0  0  8  0  0  8  8  0  0  8  8  8  8  0  0  8  8  8  0  0  8  8  8  8  8  0  0  0  8  0  8  8  0  0  0  0  0  0  8  8  8  8  0  0  0

generates a code of length 72 over Z16 who´s minimum homogenous weight is 68.

Homogenous weight enumerator: w(x)=1x^0+56x^68+908x^72+56x^76+2x^80+1x^128

The gray image is a code over GF(2) with n=576, k=10 and d=272.
This code was found by Heurico 1.16 in 79.5 seconds.