The generator matrix

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

generates a code of length 87 over Z16 who´s minimum homogenous weight is 81.

Homogenous weight enumerator: w(x)=1x^0+104x^81+352x^82+690x^83+899x^84+768x^85+992x^86+832x^87+956x^88+720x^89+788x^90+562x^91+272x^92+116x^93+52x^94+12x^95+15x^96+16x^97+6x^98+12x^99+16x^100+4x^103+4x^105+2x^114+1x^116

The gray image is a code over GF(2) with n=696, k=13 and d=324.
This code was found by Heurico 1.16 in 1.68 seconds.