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

generates a code of length 88 over Z16 who´s minimum homogenous weight is 82.

Homogenous weight enumerator: w(x)=1x^0+153x^82+164x^83+238x^84+172x^85+493x^86+556x^87+628x^88+608x^89+474x^90+164x^91+157x^92+68x^93+61x^94+44x^95+53x^96+16x^97+27x^98+6x^100+8x^102+4x^104+1x^148

The gray image is a code over GF(2) with n=704, k=12 and d=328.
This code was found by Heurico 1.16 in 1.71 seconds.