The generator matrix

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

generates a code of length 89 over Z16 who´s minimum homogenous weight is 82.

Homogenous weight enumerator: w(x)=1x^0+123x^82+408x^83+827x^84+1042x^85+1532x^86+1582x^87+1943x^88+1844x^89+1988x^90+1468x^91+1383x^92+870x^93+636x^94+300x^95+165x^96+100x^97+53x^98+40x^99+30x^100+12x^101+18x^102+8x^103+2x^104+4x^105+2x^111+1x^112+2x^118

The gray image is a code over GF(2) with n=712, k=14 and d=328.
This code was found by Heurico 1.16 in 5.71 seconds.