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

generates a code of length 84 over Z16 who´s minimum homogenous weight is 74.

Homogenous weight enumerator: w(x)=1x^0+212x^74+24x^75+470x^76+68x^77+568x^78+216x^79+703x^80+268x^81+1312x^82+2504x^83+3931x^84+2444x^85+1264x^86+328x^87+635x^88+212x^89+442x^90+64x^91+309x^92+16x^93+200x^94+101x^96+58x^98+25x^100+4x^102+4x^106+1x^116

The gray image is a code over GF(2) with n=672, k=14 and d=296.
This code was found by Heurico 1.16 in 43.9 seconds.