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

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

Homogenous weight enumerator: w(x)=1x^0+129x^68+234x^70+24x^71+560x^72+120x^73+570x^74+432x^75+889x^76+944x^77+2824x^78+1600x^79+7195x^80+1952x^81+6986x^82+1584x^83+2979x^84+976x^85+708x^86+424x^87+664x^88+104x^89+366x^90+32x^91+270x^92+72x^94+83x^96+14x^98+19x^100+2x^102+8x^104+1x^108+1x^112+1x^116

The gray image is a code over GF(2) with n=648, k=15 and d=272.
This code was found by Heurico 1.16 in 38.9 seconds.