The generator matrix

 1  0  1  1  1  6  1  1 12  1  1 10  1  1  0  1  1  6  1  1 12  1  1 10  1  1  0  1  1  6  1  1 12  1 10  1  1  1  1  1  1  1  1  1  0  6 12 10  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1
 0  1  3  6  5  1 15 12  1 10  9  1  0  3  1  6  5  1 12 15  1 10  9  1  0  3  1  6  5  1 12 15  1 10  1  9 13  3  1 15  0  6 12 10  1  1  1  1  5 11  7  9  5  3  9 15  3  5 13 11 15  7  9  1  8  4 14  2  0 12  6 14
 0  0  8  0  0  0  0  8  8  8  8  8  0  0  0  0  0  0  8  8  8  8  8  8  0  0  0  8  8  8  0  8  0  8  8  0  8  0  0  8  8  0  8  0  8  0  8  0  0  8  8  0  8  8  0  0  0  0  8  8  0  0  8  8  8  8  8  0  8  0  0  0
 0  0  0  8  0  8  8  8  8  0  8  0  8  0  8  0  8  0  0  8  0  8  0  8  0  0  8  8  8  0  8  0  0  0  8  8  0  8  0  8  8  0  0  8  8  0  0  8  0  0  0  8  8  8  0  8  8  8  0  8  0  0  8  0  0  8  0  8  8  8  8  8
 0  0  0  0  8  0  8  8  8  8  0  8  0  8  0  0  8  0  8  0  8  8  0  8  8  0  8  0  8  0  8  8  8  0  0  0  8  0  0  8  0  8  0  8  0  8  0  8  0  8  0  8  0  8  8  0  8  0  0  0  0  8  8  8  0  0  8  0  8  0  8  0

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

Homogenous weight enumerator: w(x)=1x^0+244x^68+64x^69+240x^70+64x^71+820x^72+64x^73+240x^74+64x^75+244x^76+1x^80+1x^96+1x^112

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 0.244 seconds.