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

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

Homogenous weight enumerator: w(x)=1x^0+46x^68+66x^69+185x^70+190x^71+366x^72+328x^73+663x^74+444x^75+1470x^76+910x^77+3110x^78+2466x^79+4466x^80+3510x^81+4426x^82+2438x^83+3073x^84+994x^85+1498x^86+406x^87+604x^88+248x^89+244x^90+156x^91+164x^92+78x^93+87x^94+42x^95+41x^96+10x^97+18x^98+2x^99+7x^100+7x^102+2x^104+1x^106+1x^110

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 37.9 seconds.