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

generates a code of length 84 over Z16 who´s minimum homogenous weight is 76.

Homogenous weight enumerator: w(x)=1x^0+63x^76+150x^78+16x^79+237x^80+120x^81+362x^82+624x^83+1068x^84+640x^85+346x^86+128x^87+111x^88+8x^89+86x^90+49x^92+32x^94+25x^96+16x^98+12x^100+1x^104+1x^144

The gray image is a code over GF(2) with n=672, k=12 and d=304.
This code was found by Heurico 1.16 in 1.12 seconds.