The generator matrix

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

generates a code of length 79 over Z16 who´s minimum homogenous weight is 72.

Homogenous weight enumerator: w(x)=1x^0+115x^72+410x^73+724x^74+1092x^75+1485x^76+1538x^77+2050x^78+1858x^79+2200x^80+1456x^81+1370x^82+768x^83+482x^84+378x^85+176x^86+106x^87+61x^88+50x^89+27x^90+16x^91+5x^92+8x^93+2x^94+3x^96+2x^98+1x^106

The gray image is a code over GF(2) with n=632, k=14 and d=288.
This code was found by Heurico 1.16 in 4.54 seconds.