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  1  1  1  1  1  1  1  1  1  1  2  2  2  1  2  2  1  1  1  1  2  2  2  2  1  2  1  1  4  2  1  1  2  4  1  1  8  4  2  1  1  4  4  1  4  2  2  1  8  1  1  4  1
 0 12  0  0  0  0  0  0  0  0  8  4 12 12  8  0 12 12  4  4  8  4  0 12 12  4  4  4 12  8  8  4 12  8  4 12  8  0  0  0  4 12  4  4 12  4 12 12 12 12  0  4  8  0 12  4 12  4  8  4 12 12 12 12  8  0 12  4 12  4  8  8  4  8  4 12  8  4  0  8 12  8
 0  0 12  0  0  0  0  0  0  0 12  8  4 12  4  4  4 12  0  8 12 12  4  4 12  8  0 12  0  4 12  0  8  0  8 12  4  4 12  8  8  0 12  0 12  0  8  0  8  8  4  0  4 12  4 12 12  4 12 12  4 12  8  0  0  4 12 12 12  8 12  4  0  8  4  8  8  0  4  8  0 12
 0  0  0 12  0  0  8 12 12  4  4 12  8 12 12  0  8 12 12  8  0  8 12 12 12  0  4  0  4  4  8  0 12  0  8  8  4  8  0  4 12 12  8  8 12  4  0 12  4  0  0  8  0  8  4  4  0 12  4 12 12  8  0 12  4  8  8 12  8  8  8  8 12  8 12  8 12  0 12  4  8  4
 0  0  0  0 12  0 12 12  4  8  0  0  0  0  8  0 12  4  4 12  4  0  4 12  0 12 12 12  8 12  4  0  8  0 12  8  4  8  8  0 12  0  8  0 12  8  0 12  8 12  0  4  4 12  8  4 12  0  8 12  4  8  8  0  4  8 12  4  0  0 12  4  0 12 12 12 12  8 12  8  0 12
 0  0  0  0  0 12  4  8  4  4  0  0  0  0  4  4  0  8  4  4  0  4 12 12 12  8  8 12  4  0 12  4  4  8  0  8  0  0 12  8 12 12  4  4  4  4  0 12  0 12 12  8 12  8  4  4  8  4  8  4  8  8  0  8 12 12  0  4 12  8  8 12 12 12  0  8  0 12  0 12  8  4

generates a code of length 82 over Z16 who´s minimum homogenous weight is 72.

Homogenous weight enumerator: w(x)=1x^0+233x^72+12x^73+396x^74+52x^75+610x^76+308x^77+944x^78+956x^79+1667x^80+1744x^81+2694x^82+1784x^83+1746x^84+932x^85+802x^86+252x^87+495x^88+76x^89+274x^90+28x^91+180x^92+106x^94+52x^96+28x^98+7x^100+4x^102+1x^116

The gray image is a code over GF(2) with n=656, k=14 and d=288.
This code was found by Heurico 1.16 in 13.1 seconds.