The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+288x^72+240x^73+580x^74+496x^75+1135x^76+800x^77+1148x^78+800x^79+1120x^80+496x^81+572x^82+240x^83+248x^84+4x^86+16x^88+1x^92+2x^96+4x^104+1x^112

The gray image is a code over GF(2) with n=624, k=13 and d=288.
This code was found by Heurico 1.16 in 93.8 seconds.