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  2  1  1  1  1  1  1  1  1  1  2  1  1  2  4  1  1  1  1  1  4  1  4  1  1  2  0  1  4  1  4  1  4  1  2
 0 12  0  0  0  4 12  4  8 12  8 12  0  4  8 12  0 12  0 12  8  0 12  4  0  0  8  4  8 12  4 12  0  0  4  4 12  8  4  0  4  0  8  8  8 12  8  4 12 12  8  4  4  8  8  8  0  0  0 12 12  4  0  0  4  4  0  0  0  8  4  0  4  8  8  4  0  0  4
 0  0 12  0  4  4  4  8  0  4  8  4  4  0 12  8  0 12 12  0  0 12 12  8  0 12  8  8 12 12 12  0  0  4 12  4  8  8 12  4  4  4  0  0  8  0  4  8  4 12  8  8 12  0 12 12 12 12 12 12  4  0  8 12 12  8  4  0  4 12  4  8  8 12  8 12  4 12  0
 0  0  0 12  4  0  4  4  8  0 12  4  4  4  8  8  8  8  4  4  4  0 12  0  0  8  4  4  4  8 12  8  0 12  8  0  8 12  4 12  0  0 12  8 12  8  4  8  8  0  8 12  4  0  4  0  4  8  8 12  8 12  0 12  0  8  4  4  0 12 12  8 12  0 12  8  0  4 12
 0  0  0  0  8  0  0  8  8  8  0  0  0  0  0  0  0  0  0  0  8  8  8  8  8  8  8  8  8  8  8  8  0  8  0  8  0  8  8  0  0  0  0  0  0  8  8  8  8  0  8  0  0  0  0  8  8  8  0  0  8  8  0  8  8  0  0  0  0  8  8  0  0  0  8  0  8  8  8
 0  0  0  0  0  8  0  0  0  0  8  8  0  8  8  8  8  0  8  0  8  8  8  8  8  0  0  8  8  8  0  0  8  0  8  0  0  8  8  8  0  8  0  0  8  8  8  0  8  0  8  0  8  8  8  8  8  0  8  0  0  8  8  8  0  8  8  0  0  0  0  0  0  8  0  0  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+144x^72+4x^73+192x^74+132x^75+341x^76+352x^77+666x^78+552x^79+638x^80+388x^81+292x^82+84x^83+119x^84+24x^85+60x^86+44x^88+36x^90+19x^92+2x^94+5x^96+1x^132

The gray image is a code over GF(2) with n=632, k=12 and d=288.
This code was found by Heurico 1.16 in 16.8 seconds.