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  8  1  1  1  1  0  2 12  2  0  2  2
 0  2 12  6  0  6 12 10  0  6 10 12  8 14  4 10  0  6 10 12  6  0 10 12  0  6 10 12  8 14  4  2  0  6 12 10  4 14  0  2  6  8 10  4  2 12  8 14  0  8  0  8  6 14  6 14 12 12  4  4  8 10 10  2  2  2  6  2 10  2  6  0
 0  0  8  0  0  0  8  0  0  0  0  8  0  0  8  0  0  8  8  8  8  0  8  8  8  8  8  0  8  8  0  8  0  0  0  0  0  8  8  8  0  0  0  0  8  0  8  8  8  8  8  8  0  8  8  0  0  8  8  0  0  0  8  8  0  0  0  0  0  8  8  0
 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  0  8  8  0  8  0  8  0  0  8  8  8  0  8  0  8  8  8  8  0  0  8  8  0  8  0  8  0  0  8  0  8  8  0  0  0  0  0  0  0  0  0  8  8  0  0
 0  0  0  0  8  0  8  0  0  8  8  8  8  8  0  8  8  0  0  0  8  8  8  0  8  8  8  0  8  0  0  0  0  0  0  8  8  8  0  0  8  0  0  8  8  0  0  0  0  8  0  8  8  0  8  0  8  8  8  8  0  0  8  0  8  0  0  8  8  0  0  0
 0  0  0  0  0  8  0  8  8  8  0  8  8  0  8  8  0  0  8  0  0  8  8  8  8  0  8  8  0  0  0  8  8  0  0  0  0  8  8  0  0  0  0  8  0  8  0  8  0  8  8  0  8  8  8  8  8  8  0  0  0  8  0  0  8  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+138x^68+192x^69+352x^70+192x^71+486x^72+192x^73+160x^74+64x^75+78x^76+128x^77+64x^78+1x^128

The gray image is a code over GF(2) with n=576, k=11 and d=272.
This code was found by Heurico 1.16 in 0.392 seconds.