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  2  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  1  1  1  1  1  1  1  0  1  1  2  1 12  1  2  1  0  1  1  1  0  2  1  1  0  0
 0  2  0  2  0  8 10  2  4  6  4 14 12  4  6  6  0 10  4  6  6  8  8 10  4 10  4  2  8  6 12 14  0  4 14 14  8  4  6  6 12  0  4  2  0  0 10  2  2  6  6  2 12  4  0 10 10  0  8  8  6  2  6  2  4  4 10  0  8 14 10  2  4 12 14  2  2
 0  0  2  2 12 14  6  4  4 14  2  0  8 14 10  4  0 10 10  8 10 14  4  0  8  6 14 12 10 14  4 12  6  4  0 14  6  0 10  4 14  4  2 12  8 14 10  2  0  6 14  6  6 10 10 14  8  2  2  8  0 10 10  6  0 14 12  2 10  6 14 12 14  0 14 14  6
 0  0  0  8  0  0  8  0  8  0  8  8  8  8  0  8  0  8  0  0  0  8  8  8  0  0  8  0  0  8  8  8  8  0  8  0  8  8  8  0  0  0  8  8  8  0  0  0  0  8  8  8  0  0  8  0  8  8  8  8  0  0  8  0  0  8  0  0  0  0  0  8  0  0  8  0  8
 0  0  0  0  8  8  8  8  8  8  0  0  0  8  0  8  8  8  0  8  8  8  8  8  0  0  0  0  8  0  0  0  8  8  8  0  0  8  0  8  8  0  8  8  0  0  8  0  8  8  8  0  0  8  0  8  0  8  0  8  0  0  8  0  8  0  0  0  0  0  0  0  0  8  0  8  0

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

Homogenous weight enumerator: w(x)=1x^0+378x^72+48x^73+456x^74+248x^75+782x^76+424x^77+704x^78+264x^79+376x^80+40x^81+244x^82+92x^84+32x^86+1x^88+4x^90+1x^92+1x^132

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 19.5 seconds.