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  2  8  2  1  1  8  2  1  2 12  8  1  4  1  2  1  1  8  2  1  4  1  4  1  0  2  2  1  1  1  1  4  1  8  1
 0  2  0  0  0  2  6 14  8  8 14  6 12 10  8  6 12 14  6 14  0  0 10 12 12  4 14  2 12 14  2  4  4 14 14  4  2  6  2 10 14 12  8  8  8  0  2  8  2  0  2 10  2  0 10 10 12  0  4  2 10
 0  0  2  0  2  2 10  0 12 14  8  2 12 12  2 14  2 10 14  0  4  6 12 12  0 14 10 14  2 14  8  2  0 12  8  2 12  4  6 10  2  4  8 12  8  2  6 12  4  4 14  2  2 14 14 14  2  2 10 12 10
 0  0  0  2  2  8 10  2  4  0 14 12  2  0  6  6  8  8  2  4 14  2 14  0  6  0  0  4 12 12 12  8  2 10 12 10 14  6  8 14 14 12 14  2 14  4  6  8 10  0 10 14 12  2  2  0  2  4  2  6  0
 0  0  0  0  8  8  0  8  8  8  0  0  8  8  0  8  8  0  8  8  0  0  0  8  8  0  0  8  0  8  0  8  0  8  8  0  0  0  8  0  8  8  0  0  8  0  8  0  8  8  0  0  8  8  0  8  8  8  0  8  8

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

Homogenous weight enumerator: w(x)=1x^0+174x^54+336x^55+668x^56+884x^57+1542x^58+1472x^59+2403x^60+1684x^61+2568x^62+1408x^63+1236x^64+724x^65+536x^66+272x^67+256x^68+92x^69+52x^70+32x^71+27x^72+8x^73+6x^74+2x^78+1x^84

The gray image is a code over GF(2) with n=488, k=14 and d=216.
This code was found by Heurico 1.16 in 4.6 seconds.