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

generates a code of length 86 over Z16 who´s minimum homogenous weight is 78.

Homogenous weight enumerator: w(x)=1x^0+56x^78+212x^80+278x^82+160x^83+618x^84+352x^85+878x^86+352x^87+590x^88+160x^89+190x^90+102x^92+42x^94+51x^96+28x^98+22x^100+2x^104+1x^108+1x^140

The gray image is a code over GF(2) with n=688, k=12 and d=312.
This code was found by Heurico 1.16 in 1.19 seconds.