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  0  1  2  1  1  1  1  8  2  1  1  1  1  2  1  1  2  1  8  1  2  1  2  1  1  1  2  4  1  1  1  1  1  2  1  1  1  1  1  4  2  1  2  1  2  1  1  2  2  2  2  1
 0  2  0  6  4  6 12  2  8  6  0  6  4  4  2 10 14  0 12  2  8 10 10 12 10  4 14  0  6  2  6  6  4  4  0  8  2 14  4 14  6  6  2  0  4  6 14  2  6 10 14 12  6 10 10 14  2 10 10 10 12 10  6  4 12  8 14 12  0 12 14  6  8 14  6  2 14  2  4 14  0
 0  0 12  0  4  0  0  0  8  4  4 12  8 12  4 12  0  0  8  8  8  8  4 12 12 12  4 12 12 12  0 12 12  8  4  0  8 12  4  0 12 12 12  0 12  8  8 12  0  0  0 12 12  0  4  0 12  8  4  4  0  0  8 12 12  8  8  0 12  0 12  8  0  4  8 12  4  4  4  0  0
 0  0  0 12  0  0  8 12 12  4 12  0  4 12  8 12 12  8  0 12 12  0  4  4  0  0 12  4  8 12  0 12  0  4  8  4  4  8  4 12 12  0  8  0  4  8  4  0  8  0  4  4 12  8  0 12  8  0  0  4 12  0  8  4  8  0 12  0  8 12 12  4 12  8 12  4  4  8  4 12  8
 0  0  0  0  8  0  8  8  0  0  0  8  8  8  8  0  8  8  0  0  0  8  8  8  0  8  8  0  0  0  8  8  0  8  8  8  0  8  8  0  0  8  8  8  0  8  8  0  0  0  8  8  8  0  8  0  0  8  0  8  0  8  8  0  0  0  8  0  8  0  0  8  0  0  0  0  8  0  8  0  0
 0  0  0  0  0  8  0  0  0  0  0  0  0  0  8  8  8  8  8  8  8  0  8  8  0  8  0  8  8  0  8  0  8  8  0  0  0  8  0  8  0  8  0  8  0  8  0  0  0  0  8  0  8  8  0  8  8  8  8  0  0  0  0  8  0  8  8  0  0  8  8  8  0  0  8  8  0  0  8  0  0

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

Homogenous weight enumerator: w(x)=1x^0+50x^73+129x^74+238x^75+396x^76+368x^77+705x^78+426x^79+1600x^80+486x^81+1656x^82+410x^83+723x^84+300x^85+206x^86+170x^87+139x^88+58x^89+46x^90+26x^91+15x^92+14x^93+5x^94+8x^95+4x^96+2x^97+4x^98+2x^99+2x^100+2x^101+1x^122

The gray image is a code over GF(2) with n=648, k=13 and d=292.
This code was found by Heurico 1.16 in 2.41 seconds.