The generator matrix

 1  0  1  1  1  6  1  1 12  1  1 10  1  0  1  1  1  6 12  1  1  1 14  1  1  2  1  1  8  1  6  1  1  1  1  1  2 12  1 14  1  0  1 14  1  4  1  1  1  8  1  1  1  1  1  1  1 12  1  1 14 14  1  2  0  1  1  1 12  1  1 14  1  1  6 14 10 12  1  1  1
 0  1 11  6 13  1  7  8  1 14  1  1  4  1 11  2 13  1  1  2  7  8  1  5  9  1 12  3  1  6  1  9 10 15  6  6  1  1  0  1  7  1  3  1 11  1  0  2  1  1  0  9 11  5 14  0  5  1 10 12  1  1  5  1  1  6  7 10  1 15 11  1 14 10  1  1  1  1 14 13 10
 0  0 12  0  4  0  4  4  0 12  4  8  4  4  8  0  8  4  4  4  8  0  4 12  0 12  8  8  0  8  8 12 12 12  8 12  8  8  4 12  0  4  8  8  4 12 12  0  0  4 12  0  4 12  4  0  0  8  8  4 12 12 12  4 12 12  4 12  8  0  0  8  4  0  0  8  0  8  8  8 12
 0  0  0 12  0  0  8  0  8  8  0  8  8  4 12 12 12 12  4  8  4  4  8  4  0  8  0  8 12  0 12  4 12 12  0  4 12  8  4  0  0  8  8 12 12  8 12 12 12 12  0  8 12 12  8  8 12  8 12  0  4  4 12  0  8  8  0 12  0  0  4  4  0  0  0 12  4 12  4  4  4
 0  0  0  0  8  0  0  0  8  0  8  8  8  8  0  8  8  0  0  8  8  8  0  8  8  8  8  8  8  8  0  0  8  0  0  0  0  0  8  8  8  0  0  8  8  8  0  0  0  8  8  0  8  8  0  8  8  0  8  8  8  0  0  0  0  8  0  0  0  0  8  8  8  8  8  8  8  0  8  0  0
 0  0  0  0  0  8  8  0  0  8  8  8  0  0  0  0  0  0  8  8  8  8  0  0  8  8  0  0  0  8  0  8  0  0  8  0  8  0  0  8  0  8  8  8  8  8  8  8  0  0  8  8  0  8  0  8  8  8  8  8  8  8  8  8  0  0  8  8  8  8  0  0  8  0  0  0  8  8  0  0  0

generates a code of length 81 over Z16 who´s minimum homogenous weight is 74.

Homogenous weight enumerator: w(x)=1x^0+229x^74+240x^75+743x^76+792x^77+1577x^78+1488x^79+2404x^80+1616x^81+2364x^82+1488x^83+1504x^84+792x^85+644x^86+240x^87+155x^88+27x^90+38x^92+13x^94+10x^96+8x^98+6x^100+2x^102+1x^104+1x^108+1x^112

The gray image is a code over GF(2) with n=648, k=14 and d=296.
This code was found by Heurico 1.16 in 40.6 seconds.