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

generates a code of length 84 over Z16 who´s minimum homogenous weight is 78.

Homogenous weight enumerator: w(x)=1x^0+53x^78+96x^80+168x^82+384x^83+654x^84+384x^85+180x^86+63x^88+44x^90+17x^92+3x^94+1x^164

The gray image is a code over GF(2) with n=672, k=11 and d=312.
This code was found by Heurico 1.16 in 0.674 seconds.