The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+169x^72+276x^73+686x^74+644x^75+957x^76+892x^77+1072x^78+832x^79+956x^80+708x^81+558x^82+188x^83+135x^84+44x^85+36x^86+10x^88+16x^90+4x^92+6x^96+2x^104

The gray image is a code over GF(2) with n=624, k=13 and d=288.
This code was found by Heurico 1.16 in 1.5 seconds.