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  1  1  1  1  1  1  1  1  1  2  1  2  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  1  2  1  1  1  1  1  1  2  1  2  2  1  4  1  2  2  1  1  4  1  1  1  1  8  1  1  2  2  2  2  1  1
 0 12  0  0  0  0  0  0  0  4 12 12  4 12  4 12  8 12  8 12  0  8 12  8  4 12  8  4  0  4 12  8  8  0  0  4  4  8  8  8  0 12  8 12  4  0  4  4 12 12  0  8  0  4 12 12  8  0  4 12  4  8  0 12  8  8  0  4  8 12  4  8  8  0 12  4  8  4 12 12  8  8  4  0  4  4 12  8  0
 0  0 12  0  0  8 12 12  4  4  4  8  4 12  0  8  0  8  0  4  4  4  4  4 12  0 12  4  8  0  8  0  0  4  4 12 12  4  4 12 12 12  0  8  8  8  0 12  0 12  0  4 12 12  4  4  0  8  8  0  4 12 12  8 12  0  8  0 12  0  8 12  0  8 12  8 12  8  0  8  8 12  0  4  4  8  4  0  8
 0  0  0 12  0 12 12  4  8  0  0  0  4 12  4  4  8 12  4  4  8  8  4  4  0  8  4  8  0  0  4 12 12 12  0  0 12  8  0 12  4  8  4  0  8  0 12  4 12  8 12 12  8  0  4 12  0  4 12  8 12  0  0  8  8  0 12  0  4  0  8 12 12  4 12  8  4 12  0 12  4  8  4 12 12  0  4 12  4
 0  0  0  0 12  4  8  4  4  0  4  4  4  0  8 12 12  8  8  4  8 12  0 12  4 12  0  0  8  0  4  4  0  8  4  0  4  0  8 12  4  4  4 12  0  0 12  8  0  0  4  4  8 12 12  0 12  8  0  0  8  4 12  8  4  0  4  4 12  8  4  0  8  8 12 12  8  4 12  0  4  8  4 12  4  4  0  8 12

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

Homogenous weight enumerator: w(x)=1x^0+40x^81+75x^82+80x^83+126x^84+148x^85+192x^86+356x^87+663x^88+872x^89+676x^90+332x^91+158x^92+94x^93+62x^94+54x^95+21x^96+22x^97+30x^98+34x^99+20x^100+6x^101+18x^102+6x^103+1x^104+2x^105+2x^106+2x^107+2x^112+1x^146

The gray image is a code over GF(2) with n=712, k=12 and d=324.
This code was found by Heurico 1.16 in 1.12 seconds.