The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+113x^72+264x^73+556x^74+420x^75+617x^76+348x^77+552x^78+368x^79+408x^80+216x^81+148x^82+44x^83+17x^84+4x^85+2x^86+4x^88+4x^90+5x^92+2x^94+1x^96+1x^100+1x^104

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 0.637 seconds.