The generator matrix

 1  0  1  1  1  6  1  1 14  1 12  1  1  1  0  1  2  1  1 14  1 12  1  1  1  1  8  1  2  1  1  1  8  1  2  1  1  1  1  1  6 10  1  1  0 10  1  1  1  1  2  2  1  2  1  1  1  1  6  1  4 10  1  1 14  1  1  2  1  1  0  1  6  1  8  4  1  1
 0  1 11  6  1  1  0 11  1 14  1  5 15  0  1 14  1  5 12  1  1  1 14  7  5  8  1  7  1  6  4 13  1 15  1  2  2  1 15  2  1  1  0 13  1  1 10  9 11 14  1  1  8  1  0  7  2  3  1  4  1  1  6  5  1  6  5  1  9  8  1  9  1  3  1  8  6 11
 0  0 12  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  8  8  8  8  8  8  8  8  8  0  8  8  0 12  4 12 12  4 12 12  4 12 12  4 12 12  4 12 12  4 12 12  4 12 12  4  0  4  8  8 12  0  4  8 12  4 12  0 12  8  8  0  4  4  0  4 12 12
 0  0  0 12  0  0  0  0  8  4  8 12 12 12 12  0 12  8  4 12  4  4  8  4  8 12 12  4  0 12  0  8  8  4  0  0  8 12 12 12  4  8  8  8 12  8 12  8  4  8  4  4 12  8  0  8  8  0  4 12  4  8 12  8 12 12 12  8  8  0  4  4 12  8 12  8 12 12
 0  0  0  0  4  0  4  0  4  4 12  4  8  0  0  8  4  8 12  8  0  4  4 12  4  8 12  8 12 12  8  8  8  0  4  4  4 12  4 12  4 12  8 12  0  0  4  4  0  0  8  4 12  8 12 12 12  0 12  4  0 12  8  4  4  0  4  0  0  0 12 12  8  4  4  0  0  4
 0  0  0  0  0 12  4 12  8  4  4  0  4 12  4 12  4  0  8  8  0  0  8  4 12  0  4  8  0  0  4 12 12  8 12  4  0  8 12  0 12  0  4 12  8  8 12  4 12  8 12  8  0 12 12  0  8 12  8  4 12 12 12  4  0  4  8 12  0 12 12  4 12  4 12  0  8  0

generates a code of length 78 over Z16 who´s minimum homogenous weight is 68.

Homogenous weight enumerator: w(x)=1x^0+194x^68+36x^69+546x^70+468x^71+1533x^72+1816x^73+3474x^74+4996x^75+7242x^76+8096x^77+9172x^78+8036x^79+6929x^80+4840x^81+3622x^82+1980x^83+1286x^84+380x^85+464x^86+72x^87+167x^88+104x^90+44x^92+26x^94+8x^96+2x^100+2x^104

The gray image is a code over GF(2) with n=624, k=16 and d=272.
This code was found by Heurico 1.16 in 94.6 seconds.