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  1  1  1  1  1  1  1  1  1  1  2  1  1  2  1  1
 0 12  0 12  0 12  0 12  0 12  0 12  0 12  0 12  0 12  0 12  0 12  0 12  8  4  8  4  8  4  8  4  0 12  8  4  8  4  8  4  0 12  8  4  8  4  8  4  8  4  8 12  0  4  8  4  0  8 12  4  8  4  8  4  0 12 12  0 12 12  0  0
 0  0  8  0  0  0  8  0  0  0  0  0  8  0  8  0  0  8  0  8  0  8  0  8  8  8  8  8  8  8  8  8  8  8  8  8  0  0  0  0  8  8  8  8  0  0  0  0  0  8  0  8  8  0  8  0  8  0  8  8  8  0  0  0  0  0  0  0  0  0  8  8
 0  0  0  8  0  0  0  8  0  0  0  0  0  8  0  8  8  8  8  8  8  8  8  8  8  0  8  0  8  0  8  0  8  0  0  8  8  8  0  0  8  0  0  8  8  8  0  0  0  8  8  0  8  8  0  0  8  8  0  8  0  8  0  0  0  0  0  0  8  8  8  8
 0  0  0  0  8  0  8  0  0  8  8  8  8  8  0  8  8  0  8  0  0  8  0  8  8  0  8  0  0  8  0  8  0  8  0  8  0  8  0  8  0  0  8  8  8  0  8  8  8  0  0  0  8  0  8  0  8  8  8  0  0  8  0  0  0  0  0  8  8  0  0  0
 0  0  0  0  0  8  0  8  8  8  8  0  8  0  8  8  0  0  8  8  8  8  0  0  0  0  8  8  8  8  0  0  0  0  0  0  0  0  0  0  8  8  0  8  8  0  0  8  8  8  8  0  8  8  8  8  0  0  8  0  8  8  8  0  0  0  8  8  0  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+24x^68+80x^70+814x^72+80x^74+23x^76+1x^80+1x^140

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 0.324 seconds.