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

generates a code of length 81 over Z16 who´s minimum homogenous weight is 72.

Homogenous weight enumerator: w(x)=1x^0+112x^72+8x^73+262x^74+36x^75+363x^76+192x^77+668x^78+800x^79+1261x^80+1040x^81+1244x^82+760x^83+546x^84+160x^85+264x^86+64x^87+153x^88+8x^89+116x^90+4x^91+63x^92+32x^94+25x^96+6x^98+3x^100+1x^124

The gray image is a code over GF(2) with n=648, k=13 and d=288.
This code was found by Heurico 1.16 in 2.68 seconds.