The generator matrix

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

generates a code of length 77 over Z16 who´s minimum homogenous weight is 72.

Homogenous weight enumerator: w(x)=1x^0+264x^72+72x^73+807x^74+152x^75+745x^76+112x^77+791x^78+80x^79+687x^80+72x^81+189x^82+24x^83+91x^84+5x^86+3x^96+1x^104

The gray image is a code over GF(2) with n=616, k=12 and d=288.
This code was found by Heurico 1.16 in 10.8 seconds.