The generator matrix

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

generates a code of length 78 over Z16 who´s minimum homogenous weight is 71.

Homogenous weight enumerator: w(x)=1x^0+98x^71+380x^72+704x^73+974x^74+1592x^75+1481x^76+2290x^77+1666x^78+2216x^79+1437x^80+1592x^81+776x^82+520x^83+277x^84+134x^85+126x^86+42x^87+37x^88+14x^89+6x^90+8x^91+1x^92+4x^94+4x^95+1x^96+2x^97+1x^108

The gray image is a code over GF(2) with n=624, k=14 and d=284.
This code was found by Heurico 1.16 in 4.45 seconds.