The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+110x^71+798x^72+1362x^73+2261x^74+2818x^75+3617x^76+3526x^77+4244x^78+3514x^79+3586x^80+2514x^81+2053x^82+1184x^83+645x^84+260x^85+125x^86+36x^87+47x^88+16x^89+14x^90+18x^91+10x^92+2x^93+7x^94

The gray image is a code over GF(2) with n=624, k=15 and d=284.
This code was found by Heurico 1.16 in 12.9 seconds.