The generator matrix

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

generates a code of length 72 over Z16 who´s minimum homogenous weight is 67.

Homogenous weight enumerator: w(x)=1x^0+394x^67+516x^68+970x^69+922x^70+882x^71+1071x^72+996x^73+856x^74+622x^75+359x^76+352x^77+72x^78+70x^79+32x^80+44x^81+4x^82+16x^83+5x^84+6x^85+2x^94

The gray image is a code over GF(2) with n=576, k=13 and d=268.
This code was found by Heurico 1.16 in 74.9 seconds.