The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  8  1  1  2  1  1  1  1  8  1  1  1  1  2  1  0  1  1  2  1  1  1  1  8  1  1  1  1  2  2  1  2  1  1  1  2  1  1  1  4  1  2  1  8  1  8  1  2  2  1  2  1  1  1  4  8  1  0  1
 0  2  0  6  0 14 10  8  6  8  2  8  0  6  8  2  4  6  2  4 10 12  2  4 14 14  0 12  0 14  2 14  6  6  8 12 14  8  2 14 12 14 10 14  6  2 12 12  6  6  8 12  2  2  0  6 10  6 14 14 10  4  8 10 12 10  2  6  6  2  8  0  0  2 10  2  8  6 14  6 10 12 14  2  2  2  8  2  0
 0  0 12  0  0  0  0  4  4  8  4  4  8  4 12  4  4  0  8  0 12  4  0  8 12 12  0  4 12  4  8  4  8  0  0  4  4  0  4  0  8  4 12  8  8  4  8  8 12  0 12  8  8  0  4 12 12  0  0  8 12  0 12  0  0  4 12  8 12 12  0 12  4  4 12  0  4  8 12  8  4  8  8  8  8  8 12  8  0
 0  0  0 12  0  8 12  0 12  4 12 12  4  0 12  8 12  4 12  4  0  4  8 12  4  8  8  0  0  4  4 12  0 12  0 12  8  4  0 12  4  0 12 12  4  4  0  8  8  0  8  8  8  0  4 12  4  4  8  0  8  0  8 12  4  0  0  0  4 12  4  4 12  0  8  4  8  4 12  4 12 12  8  0  8  4 12  0  8
 0  0  0  0 12 12  4 12  8  0 12  4 12 12  8  0 12  4  0  8  4  8  8  4  0  0 12  8 12 12  0  4 12 12  8  0  4  8  0  8  4  8  0  8  4  0  8  4  4  8  0 12  4 12 12  0  4  8  8 12  8  4  4 12  0 12 12  4  4 12 12  0 12  8  4  4  0 12  0  8  0 12  0  8  0  4  0  0  8

generates a code of length 89 over Z16 who´s minimum homogenous weight is 81.

Homogenous weight enumerator: w(x)=1x^0+52x^81+122x^82+278x^83+372x^84+472x^85+617x^86+746x^87+973x^88+1118x^89+992x^90+704x^91+574x^92+408x^93+271x^94+190x^95+107x^96+78x^97+32x^98+20x^99+8x^100+6x^101+10x^102+8x^103+11x^104+8x^105+2x^106+6x^107+2x^108+2x^109+1x^110+1x^134

The gray image is a code over GF(2) with n=712, k=13 and d=324.
This code was found by Heurico 1.16 in 2.64 seconds.