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

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

Homogenous weight enumerator: w(x)=1x^0+50x^64+58x^65+91x^66+54x^67+179x^68+170x^69+537x^70+514x^71+884x^72+514x^73+551x^74+110x^75+124x^76+50x^77+69x^78+22x^79+33x^80+28x^81+19x^82+4x^83+9x^84+12x^85+8x^86+3x^90+1x^94+1x^118

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 0.814 seconds.