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  8  1  1  1  1  1  1  1  1  1  1  8  1  1  1  1  1  1  8  1  1  1  1  4
 0  2  0  6  4 14 12  2  4  6  8 10  0  6  4  2  0  6 12 10  8 14  4  2  8 14  4  2  4  2  8 14  0  6  0  6  4  2 12 10 12 10  8 14  8 14  4  2  4 10  4 12 10 12  2  4  2  0  0  8  0  6  6  6  0  6  4  2 14  0 12 12
 0  0 12  0  4  4  0  4 12  0  4  0  0 12  0 12  8  8  8  8  4  4 12 12  8  8  8  8  4  4 12 12  0  0 12 12  4 12  8  0 12  4  4  4  0  8  0  8 12 12  4  0  8 12  0  8  4  8  4  0  8  8 12  4 12  0  4  4  4  0  0  0
 0  0  0  8  0  0  8  8  8  8  8  0  8  0  0  8  8  8  8  0  0  0  0  8  0  8  0  0  8  8  8  0  0  0  0  8  8  0  8  8  8  0  8  8  8  0  8  8  8  0  0  0  8  0  8  0  0  0  0  0  8  0  8  8  8  0  8  0  8  8  0  0
 0  0  0  0  8  0  0  0  0  8  8  8  8  8  8  8  8  0  0  8  0  8  8  0  0  8  8  0  0  8  8  0  8  0  8  0  8  0  8  0  8  0  0  8  0  8  8  0  8  8  0  0  8  0  8  0  8  8  8  0  0  0  8  0  0  8  0  0  0  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+193x^68+536x^70+64x^71+486x^72+384x^73+104x^74+64x^75+115x^76+80x^78+4x^80+16x^82+1x^136

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 0.598 seconds.