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

generates a code of length 68 over Z16 who´s minimum homogenous weight is 56.

Homogenous weight enumerator: w(x)=1x^0+81x^56+102x^57+181x^58+274x^59+374x^60+480x^61+697x^62+944x^63+1689x^64+2340x^65+2916x^66+3996x^67+4534x^68+4096x^69+3013x^70+2426x^71+1640x^72+956x^73+585x^74+428x^75+340x^76+182x^77+184x^78+110x^79+92x^80+34x^81+38x^82+14x^83+16x^84+2x^85+1x^86+1x^88+1x^94

The gray image is a code over GF(2) with n=544, k=15 and d=224.
This code was found by Heurico 1.16 in 29.6 seconds.