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

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

Homogenous weight enumerator: w(x)=1x^0+172x^72+16x^73+364x^74+128x^75+685x^76+352x^77+832x^78+384x^79+528x^80+144x^81+254x^82+112x^84+70x^86+34x^88+14x^90+3x^92+2x^94+1x^128

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 1.24 seconds.