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

generates a code of length 81 over Z16 who´s minimum homogenous weight is 68.

Homogenous weight enumerator: w(x)=1x^0+73x^68+22x^69+78x^70+62x^71+149x^72+184x^73+153x^74+374x^75+197x^76+1006x^77+716x^78+2088x^79+1749x^80+2776x^81+1752x^82+2100x^83+695x^84+970x^85+159x^86+406x^87+117x^88+144x^89+123x^90+86x^91+55x^92+18x^93+45x^94+4x^95+30x^96+34x^98+4x^100+8x^102+2x^104+2x^106+1x^110+1x^118

The gray image is a code over GF(2) with n=648, k=14 and d=272.
This code was found by Heurico 1.16 in 11.3 seconds.