The generator matrix

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

generates a code of length 77 over Z16 who´s minimum homogenous weight is 72.

Homogenous weight enumerator: w(x)=1x^0+145x^72+324x^73+560x^74+336x^75+518x^76+368x^77+510x^78+316x^79+547x^80+306x^81+140x^82+4x^83+2x^84+8x^85+4x^86+2x^88+2x^89+1x^94+1x^104+1x^110

The gray image is a code over GF(2) with n=616, k=12 and d=288.
This code was found by Heurico 1.16 in 0.556 seconds.