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

generates a code of length 83 over Z16 who´s minimum homogenous weight is 72.

Homogenous weight enumerator: w(x)=1x^0+55x^72+132x^73+188x^74+416x^75+584x^76+836x^77+1292x^78+1676x^79+2423x^80+3148x^81+3807x^82+4028x^83+3584x^84+3116x^85+2415x^86+1734x^87+1206x^88+810x^89+460x^90+286x^91+218x^92+114x^93+66x^94+38x^95+48x^96+30x^97+24x^98+14x^99+6x^100+6x^101+3x^102+3x^104+1x^114

The gray image is a code over GF(2) with n=664, k=15 and d=288.
This code was found by Heurico 1.16 in 30.8 seconds.