The generator matrix

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

generates a code of length 78 over Z16 who´s minimum homogenous weight is 72.

Homogenous weight enumerator: w(x)=1x^0+25x^72+242x^73+212x^74+530x^75+333x^76+538x^77+416x^78+582x^79+347x^80+410x^81+127x^82+158x^83+58x^84+86x^85+11x^86+10x^87+2x^88+4x^89+1x^90+1x^92+1x^94+1x^120

The gray image is a code over GF(2) with n=624, k=12 and d=288.
This code was found by Heurico 1.16 in 0.512 seconds.