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

generates a code of length 83 over Z16 who´s minimum homogenous weight is 78.

Homogenous weight enumerator: w(x)=1x^0+140x^78+38x^80+160x^81+364x^82+704x^83+256x^84+160x^85+148x^86+24x^88+52x^90+1x^160

The gray image is a code over GF(2) with n=664, k=11 and d=312.
This code was found by Heurico 1.16 in 58.3 seconds.