The generator matrix

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

generates a code of length 81 over Z16 who´s minimum homogenous weight is 73.

Homogenous weight enumerator: w(x)=1x^0+116x^73+384x^74+846x^75+1345x^76+2038x^77+2649x^78+3222x^79+3886x^80+4170x^81+3927x^82+3200x^83+2576x^84+1816x^85+1109x^86+682x^87+338x^88+144x^89+103x^90+96x^91+36x^92+32x^93+18x^94+16x^95+6x^96+2x^98+2x^99+3x^100+2x^101+1x^104+2x^105

The gray image is a code over GF(2) with n=648, k=15 and d=292.
This code was found by Heurico 1.16 in 17.9 seconds.