The generator matrix

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

generates a code of length 72 over Z16 who´s minimum homogenous weight is 69.

Homogenous weight enumerator: w(x)=1x^0+422x^69+225x^70+384x^71+140x^72+350x^73+146x^74+260x^75+18x^76+64x^77+12x^78+8x^79+8x^81+8x^85+1x^98+1x^100

The gray image is a code over GF(2) with n=576, k=11 and d=276.
This code was found by Heurico 1.16 in 4.41 seconds.