The generator matrix

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

generates a code of length 76 over Z16 who´s minimum homogenous weight is 72.

Homogenous weight enumerator: w(x)=1x^0+509x^72+280x^73+756x^74+232x^75+642x^76+232x^77+692x^78+280x^79+405x^80+12x^82+33x^84+12x^86+8x^88+1x^108+1x^112

The gray image is a code over GF(2) with n=608, k=12 and d=288.
This code was found by Heurico 1.16 in 0.927 seconds.