The generator matrix

 1  0  1  1  1 14  1  1  8  1  1  6  1  1  1  1 12  1  0  1  1  6  1  8  1  2  1  1  1  6  1  1  1  1  1  0  1  0  1  6  1  1  1 14  4  1  1  1  4  1  1  1  1  1  1  1  2 12 12  1  1
 0  1  1  0  7  1  2 11  1 14  5  1 14  3  1  0  1 10  1  8  1  1 11  1  0  1  6  7  4  1  4  1 15  5  9  1  0  1 10  1  9  5 11  1  1  1  2  2  1  5  8 12 10 10  6  1  1  1  2  5 12
 0  0  2  0  2  4  0  2  2  8  2 14  2  4  0  6  6 10 12 14 12  8  4  6 14 14  0  0 10  8  8 12  8  6 14  6 12  0  2  6  8  4  6  8 12  8 14 14 12 10 10  0  2 12  0  4  6 12  2 14 12
 0  0  0  2  0  0 10  6  6 12  2  6 14 12 12  6  8  4  2 12 10 14  2 10  2 12  8  0  8  8  6  8 14  0  0 14 12  4 14  0  8 10 12  4  2 10  6 12  0 10  2 10  2  8  6  4 12 12  4  6  2
 0  0  0  0  8  8  8  8  8  8  0  0  8  8  0  0  8  8  0  0  0  8  8  0  0  0  0  8  0  0  8  0  0  8  0  8  8  8  0  8  8  8  8  0  8  8  8  0  8  8  8  8  8  8  0  0  8  0  0  0  8

generates a code of length 61 over Z16 who´s minimum homogenous weight is 54.

Homogenous weight enumerator: w(x)=1x^0+167x^54+410x^55+1056x^56+1588x^57+2910x^58+3134x^59+5264x^60+4280x^61+4967x^62+2954x^63+2854x^64+1490x^65+884x^66+346x^67+244x^68+108x^69+62x^70+20x^71+18x^72+6x^73+1x^76+2x^78+1x^80+1x^84

The gray image is a code over GF(2) with n=488, k=15 and d=216.
This code was found by Heurico 1.16 in 11.8 seconds.