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

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

Homogenous weight enumerator: w(x)=1x^0+228x^72+238x^74+128x^75+332x^76+768x^77+570x^78+1152x^79+225x^80+194x^82+195x^84+22x^86+42x^88+1x^148

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 9.53 seconds.