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

generates a code of length 78 over Z16 who´s minimum homogenous weight is 72.

Homogenous weight enumerator: w(x)=1x^0+42x^72+248x^73+303x^74+422x^75+357x^76+504x^77+569x^78+444x^79+361x^80+268x^81+192x^82+174x^83+46x^84+80x^85+24x^86+32x^87+16x^88+4x^89+7x^90+1x^92+1x^118

The gray image is a code over GF(2) with n=624, k=12 and d=288.
This code was found by Heurico 1.16 in 0.757 seconds.