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  2  1  1  1  1  1  1  1  1  1  2  1  1  1  1  1  2  1  1  1  1  1  1  2  1  4  1  1  2  2  4  1  1  0  1  2  1  1  1  0  2  1  2  1  4  2  2
 0 12  0  0  0  4 12  4  8 12  8 12  0  4  8 12  0 12  4  8  0 12 12  0  0 12 12  4 12  4  0  0  8  8 12  8  4  0  4  0  8  4  0  8  4  0  4 12  8 12  0  0  4  8 12  4  0  4  8 12  0  0  8  8  8  0  8 12  4  0  8  0
 0  0 12  0  4  4  4  8  0  4  8  4  4  0 12  0  0 12 12 12  0  8  0  4  8 12  0  4  8  4  4  4  0  0 12  8  8 12 12  8  4  4  0  0  0  4 12  8 12  0  4 12 12 12  0 12 12 12  4  0  8  8 12 12  0  8 12 12 12  8  8  0
 0  0  0 12  4  0  4  4  8  0 12  4  4  4  8  0  8  8 12  0 12  4  8 12  4 12 12  4  0  0  4  0  8 12  0 12  8  4  4 12 12  8  0  4 12  0  8 12 12  4 12  8 12  4  8  0  0  8  0 12 12  8  0  0  4 12 12  8  8  4 12  0
 0  0  0  0  8  0  0  8  8  8  0  0  0  0  8  8  8  0  8  8  8  8  8  0  8  8  0  8  0  8  8  0  0  8  8  0  8  0  0  0  8  0  8  8  8  0  8  0  8  8  0  8  0  0  8  8  8  0  8  8  0  0  8  0  0  8  0  0  8  8  0  0
 0  0  0  0  0  8  0  0  0  0  8  8  0  8  8  0  8  0  8  0  8  8  8  8  0  8  0  0  8  8  8  8  8  8  0  0  8  8  0  0  8  8  0  0  0  0  0  8  0  8  0  0  0  0  0  0  8  0  0  8  8  0  8  0  0  8  8  8  8  8  8  0

generates a code of length 72 over Z16 who´s minimum homogenous weight is 64.

Homogenous weight enumerator: w(x)=1x^0+57x^64+159x^66+36x^67+234x^68+176x^69+514x^70+556x^71+752x^72+560x^73+484x^74+172x^75+139x^76+32x^77+84x^78+4x^79+57x^80+33x^82+30x^84+6x^86+8x^88+1x^92+1x^112

The gray image is a code over GF(2) with n=576, k=12 and d=256.
This code was found by Heurico 1.16 in 0.792 seconds.